8916:
267:
3397:
7158:
5219:
5427:, whose variables can be seen as tacitly quantified. Whether the shallowest instance of a variable is even or odd determines whether that variable's quantification is universal or existential. (Shallowness is the contrary of depth, which is determined by the nesting of negations.) Peirce's graphical logic has attracted some attention in recent years by those researching
43:
5447:
2268:
2114:
1086:
An example of translating a quantified statement in a natural language such as
English would be as follows. Given the statement, "Each of Peter's friends either likes to dance or likes to go to the beach (or both)", key aspects can be identified and rewritten using symbols including quantifiers. So,
403:
In a first-order logic statement, quantifications in the same type (either universal quantifications or existential quantifications) can be exchanged without changing the meaning of the statement, while the exchange of quantifications in different types changes the meaning. As an example, the only
3025:
of that variable. The range of quantification specifies the set of values that the variable takes. In the examples above, the range of quantification is the set of natural numbers. Specification of the range of quantification allows us to express the difference between, say, asserting that a
5264:. He would universally quantify a variable (or relation) by writing the variable over a dimple in an otherwise straight line appearing in his diagrammatic formulas. Frege did not devise an explicit notation for existential quantification, instead employing his equivalent of ~∀
3260:
and the relation between the two, which is usually expressed as a function from syntactic objects to semantic ones. This article only addresses the issue of how quantifier elements are interpreted. The syntax of a formula can be given by a syntax tree. A quantifier has a
2121:
1967:
4245:
3922:
requires first-order predicate calculus with equality. This means there is given a distinguished two-placed predicate "="; the semantics is also modified accordingly so that "=" is always interpreted as the two-place equality relation on
6002:. Springer-Verlag. The 1928 first edition is the first time quantification was consciously employed in the now-standard manner, namely as binding variables ranging over some fixed domain of discourse. This is the defining aspect of
4939:
4695:
2790:
2687:
4569:
4807:
1285:. These two expressions (using the definitions above) are read as "there exists a friend of Peter who likes to dance" and "all friends of Peter like to dance", respectively. Variant notations include, for set
2309:
satisfies pointwise, but not uniform continuity (its slope is unbound). In contrast, interchanging the two initial universal quantifiers in the definition of pointwise continuity does not change the meaning.
5145:
1738:
Some versions of the notation explicitly mention the range of quantification. The range of quantification must always be specified; for a given mathematical theory, this can be done in several ways:
3080:
3472:
3348:
3999:
2592:
4081:
3819:
3617:
3125:
1186:
2473:
605:
720:
4087:
2526:
2404:
808:
2263:{\displaystyle \forall \varepsilon >0\;\exists \delta >0\;\forall x\in \mathbb {R} \;\forall h\in \mathbb {R} \;(|h|<\delta \,\Rightarrow \,|f(x)-f(x+h)|<\varepsilon )}
2109:{\displaystyle \forall \varepsilon >0\;\forall x\in \mathbb {R} \;\exists \delta >0\;\forall h\in \mathbb {R} \;(|h|<\delta \,\Rightarrow \,|f(x)-f(x+h)|<\varepsilon )}
1605:
1434:
860:
647:
532:
490:
1641:
362:
1568:
1399:
7295:
5043:
3038:" for real numbers, although relying exclusively on naming conventions cannot work in general, since ranges of variables can change in the course of a mathematical argument.
1677:
1534:
1022:, and Tarski's students. Relation algebra cannot represent any formula with quantifiers nested more than three deep. Surprisingly, the models of relation algebra include the
1503:
1358:
1276:
1247:
1469:
1324:
249:
171:
2998:
1703:
2871:
758:
7970:
1899:
This is clearly true; it just asserts that every natural number has a square. The meaning of the assertion in which the order of quantifiers is reversed is different:
312:
292:
214:
132:
2968:
2931:
2891:
1733:
5188:, also called Aristotelian logic, treats quantification in a manner that is closer to natural language, and also less suited to formal analysis. Term logic treated
916:, there would be no way to enumerate all the conjuncts, since irrationals cannot be enumerated. A succinct, equivalent formulation which avoids these problems uses
6275:
3181:, variables range over all sets. In this case, guarded quantifiers can be used to mimic a smaller range of quantification. Thus in the example above, to express
6280:
4839:
2911:
382:
191:
8053:
7194:
4601:
2706:
2603:
8952:
6126:
9426:
1067:
The two most common quantifiers are the universal quantifier and the existential quantifier. The traditional symbol for the universal quantifier is "
64:
51:
4469:
4710:
8367:
5394:." Peano, who was much better known than Peirce, in effect diffused the latter's thinking throughout Europe. Peano's notation was adopted by the
8525:
6034:, Dover Publications. The quantifiers are discussed in chapters §18 "Binding of variables" through §30 "Derivations from Synthetic Premises".
5912:
5642:
7313:
8380:
7703:
6658:
999:
with quantification, but progress has been slow and interest in such algebra has been limited. Three approaches have been devised to date:
5336:
9294:
8961:
6315:
6157:
6101:
3252:
to study the meaning of expressions in a formal language. It has three elements: a mathematical specification of a class of objects via
7965:
8385:
8375:
8112:
7318:
256:
7863:
7309:
5328:
8521:
6469:
6053:
5889:
5667:
5606:
5229:
82:
5312:
1015:
6085:
5070:
8618:
8362:
7187:
5994:
7923:
7616:
7357:
5236:
confirmed this in 1847, but modern usage began with De Morgan in 1862 where he makes statements such as "We are to take in both
3178:
1931:
natural number. This is because the syntax directs that any variable cannot be a function of subsequently introduced variables.
1743:
9381:
9035:
9502:
9376:
8945:
8879:
8581:
8344:
8339:
8164:
7585:
7269:
5693:
5261:
3483:
1100:
251:
expresses that there exists something in the domain which satisfies that property. A formula where a quantifier takes widest
3044:
3403:
3279:
9154:
8975:
8874:
8657:
8574:
8287:
8218:
8095:
7337:
7077:
6285:
6095:
6077:
3933:
3474:, illustrating scope and variable capture. Bound and free variable occurrences are colored in red and green, respectively.
2537:
7945:
4018:
3756:
3554:
1763:
Mention explicitly the range of quantification, perhaps using a symbol for the set of all objects in that domain (or the
9658:
8799:
8625:
8311:
7544:
7113:
7089:
6678:
3089:
2847:
1122:
7950:
9653:
9040:
8282:
8021:
7279:
7180:
6690:
6434:
6072:
2419:
2317:(or swapping two adjacent existential quantifiers with the same scope) doesn't change the meaning of the formula (see
31:
8677:
8672:
540:
9128:
2597:
Together with negation, only one of either the universal or existential quantifier is needed to perform both tasks:
9522:
9184:
9005:
8606:
8196:
7590:
7558:
7249:
6700:
4240:{\displaystyle \forall y,z{\big (}A(x_{1},\ldots ,x_{n-1},y)\wedge A(x_{1},\ldots ,x_{n-1},z)\implies y=z{\big )}.}
655:
7323:
1646:
All of these variations also apply to universal quantification. Other variations for the universal quantifier are
419:
quantifiers such as "some" and "all". However, many natural language quantifiers can only be analyzed in terms of
9527:
9477:
9239:
8938:
8896:
8845:
8742:
8240:
8201:
7678:
7108:
6665:
6561:
5232:
claimed to have coined the terms "quantify" and "quantification", most likely in his
Edinburgh lectures c. 1840.
3919:
1823:
955:
1 is equal to 5 + 5, or 2 is equal to 5 + 5, or 3 is equal to 5 + 5, ... , or 100 is equal to 5 + 5, or ..., etc.
8737:
7352:
4403:
One possible interpretation mechanism can be obtained as follows: Suppose that in addition to a semantic domain
1749:
Fix several domains of discourse in advance and require that each variable have a declared domain, which is the
9648:
9587:
9446:
9025:
8667:
8206:
8058:
8041:
7764:
7244:
7103:
6943:
6411:
6247:
6203:
5485:
2484:
2362:
6123:
4318:
5428:
1771:
One can use any variable as a quantified variable in place of any other, under certain restrictions in which
767:
9582:
9123:
8569:
8546:
8507:
8393:
8334:
7980:
7900:
7744:
7688:
7301:
7123:
6938:
6454:
6150:
5499:
5480:
5409:
5573:
5288:
1573:
9612:
9279:
9249:
9224:
9164:
9063:
8995:
8859:
8586:
8564:
8531:
8424:
8270:
8255:
8228:
8179:
8063:
7998:
7823:
7789:
7784:
7658:
7489:
7466:
7045:
7035:
6985:
6959:
6735:
6609:
6576:
6477:
6459:
6359:
6208:
6190:
6009:
5490:
5475:
5401:
5347:
5284:
3479:
2835:
2828:
1797:
Mathematical formulas mix symbolic expressions for quantifiers with natural language quantifiers such as,
1404:
1011:
813:
610:
495:
434:
420:
194:
1946:
continuity, whose definitions differ only by an exchange in the positions of two quantifiers. A function
9507:
9401:
9366:
9254:
9229:
9073:
8990:
8789:
8642:
8434:
8152:
7888:
7794:
7653:
7638:
7519:
7494:
7083:
7071:
7051:
7040:
6955:
6768:
6744:
6566:
6522:
6374:
6300:
6213:
5396:
1935:
1610:
329:
8915:
5420:
introduced the ∀ symbol, by analogy with Peano's ∃ symbol. ∀ did not become canonical until the 1960s.
4956:
A few other quantifiers have been proposed over time. In particular, the solution quantifier, noted § (
2321:), but swapping an existential quantifier and an adjacent universal quantifier may change its meaning.
1539:
1363:
1875:
The order of quantifiers is critical to meaning, as is illustrated by the following two propositions:
1075:", which stands for "for all" or "all". The corresponding symbol for the existential quantifier is "
9492:
9299:
9078:
8762:
8724:
8601:
8405:
8245:
8169:
8147:
7975:
7933:
7832:
7799:
7663:
7451:
7362:
7098:
7002:
6966:
6881:
6837:
6673:
6604:
6394:
6223:
6198:
6024:. Indiana University Press. The first appearance of quantification in anything like its present form.
5470:
5061:
4966:
2811:
1757:
1652:
1508:
1023:
112:
1474:
1329:
1252:
1223:
9577:
9542:
9487:
9431:
9334:
9319:
9289:
9269:
9244:
9113:
9098:
8891:
8782:
8767:
8747:
8704:
8591:
8541:
8467:
8412:
8349:
8142:
8137:
8085:
7853:
7842:
7514:
7414:
7342:
7333:
7329:
7264:
7259:
6976:
6875:
6822:
6798:
6721:
6624:
6556:
6482:
6295:
6290:
6267:
6242:
6111:(Covers syntax, model theory, and metatheory for first order logic in the natural deduction style.)
5975:
5460:
5257:
4408:
4378:
3174:
3018:
3001:
2937:
1943:
1439:
1299:
948:
889:
650:
535:
219:
141:
104:
2973:
1682:
9663:
9622:
9547:
9517:
9482:
9462:
9391:
9371:
9309:
9304:
9214:
9204:
9189:
8920:
8689:
8652:
8637:
8630:
8613:
8399:
8265:
8174:
8127:
7940:
7849:
7683:
7668:
7628:
7565:
7553:
7509:
7484:
7254:
7203:
7161:
7094:
6908:
6793:
6778:
6725:
6685:
6634:
6571:
6530:
6507:
6487:
6390:
6218:
6143:
5942:. CSLI (University of Chicago Press) and New York: Seven Bridges Press. A gentle introduction to
5747:
5316:
5233:
5222:
5201:
2839:
2815:
2410:
2318:
1939:
1764:
1007:
409:
405:
389:
385:
315:
96:
8417:
7873:
6067:
5882:
Outline of a new system of logic: with a critical examination of Dr. Whately's
Elements of Logic
5213:
Outline of a New System of Logic: With a
Critical Examination of Dr. Whately's Elements of Logic
1775:
does not occur. Even if the notation uses typed variables, variables of that type may be used.
882:
1 · 2 = 1 + 1, and 2 · 2 = 2 + 2, and 3 · 2 = 3 + 3, ..., and 100 · 2 = 100 + 100, and ..., etc.
2853:
725:
9602:
9557:
9537:
9497:
9436:
9406:
9386:
9179:
9108:
8855:
8662:
8472:
8462:
8354:
8235:
8070:
8046:
7827:
7811:
7716:
7693:
7570:
7539:
7504:
7399:
7234:
6980:
6817:
6807:
6783:
6760:
6716:
6642:
6594:
6552:
6512:
6354:
6349:
6171:
6049:
6003:
5989:
5943:
5908:
5885:
5739:
5699:
5689:
5663:
5638:
5602:
5452:
5424:
5332:
2818:, that is, a string of quantifiers and bound variables followed by a quantifier-free formula.
1036:
913:
393:
297:
277:
266:
199:
135:
117:
6115:
5902:
2953:
2916:
2876:
9607:
9532:
9421:
9199:
8869:
8864:
8757:
8714:
8536:
8497:
8492:
8477:
8303:
8260:
8157:
7955:
7905:
7479:
7441:
7130:
6971:
6870:
6812:
6750:
6545:
6424:
6419:
6404:
6369:
6329:
6257:
6252:
6027:
5731:
5630:
5532:
5505:
5405:
5340:
5273:
4317:); the latter formula, when interpreted over the positive integers, is known to be false by
4251:
3509:
1870:
1708:
1051:
1030:
1003:
988:
416:
397:
5390:" for "there exists at least one individual in the domain of discourse having the property
9411:
9314:
9209:
9174:
8850:
8840:
8794:
8777:
8732:
8694:
8596:
8516:
8323:
8250:
8223:
8211:
8117:
8031:
8005:
7960:
7928:
7729:
7531:
7474:
7424:
7389:
7347:
6851:
6827:
6647:
6619:
6599:
6447:
6415:
6399:
6130:
5970:
5935:
5849:
5252:
4934:{\displaystyle 0<\operatorname {P} \{w:F(v_{1},\ldots ,v_{n-1},w)=\mathbf {T} \}\leq a}
3257:
3005:
2807:
2325:
996:
894:
319:
6887:
6364:
2933:?", and the statement without quantifiers can be viewed as the answer to that question.
1794:). Formally, however, the phrase that introduces the dummy variable is placed in front.
1119:
likes to go to the beach". Then the above sentence can be written in formal notation as
9643:
9597:
9592:
9512:
9396:
9274:
9169:
9010:
8835:
8814:
8772:
8752:
8647:
8502:
8100:
8090:
8080:
8075:
8009:
7883:
7759:
7648:
7643:
7621:
7222:
6788:
6773:
6695:
6614:
6540:
6180:
6089:
5351:
5320:
5292:
5269:
5208:
3253:
3083:
2947:
2896:
968:
925:
898:
367:
176:
17:
8930:
5867:
Hehner (2004) uses the term "quantifier" in a very general sense, also including e.g.
5370:. Hence for decades, the canonical notation in philosophy and mathematical logic was (
5215:, describing the principle of the quantifier, but the book was not widely circulated.
9637:
9284:
9259:
9093:
8809:
8487:
7994:
7779:
7769:
7739:
7724:
7394:
6913:
6803:
6535:
6498:
6442:
6310:
6305:
6108:
5985:
5965:
5751:
5601:. Handbook of Theoretical Computer Science. Vol. B. Elsevier. pp. 493–574.
5526:
5432:
5413:
5324:
5247:
4690:{\displaystyle \operatorname {P} \{w:F(v_{1},\ldots ,v_{n-1},w)=\mathbf {T} \}\geq b}
4366:
3270:
3262:
2314:
1040:
1019:
912:
to generate all the conjuncts. However, if an assertion were to be made about every
252:
5720:"Range and degree of realizability of formulas in the restricted predicate calculus"
5536:
3396:
2944:
are thought of as being simpler, with the quantifier-free formulas as the simplest.
2785:{\displaystyle \neg (\exists x\!\in \!D\;P(x))\equiv \forall x\!\in \!D\;\neg P(x),}
2682:{\displaystyle \neg (\forall x\!\in \!D\;P(x))\equiv \exists x\!\in \!D\;\neg P(x),}
9552:
9472:
9339:
9219:
9103:
9083:
8709:
8556:
8457:
8449:
8329:
8277:
8186:
8122:
8105:
8036:
7895:
7754:
7456:
7239:
6925:
6344:
5549:
5494:
4957:
4267:
2843:
1951:
1204:
992:
761:
108:
5218:
9467:
9441:
9324:
9088:
9015:
8819:
8699:
7878:
7868:
7815:
7499:
7419:
7404:
7284:
7229:
7118:
6895:
6832:
6012:, 1885, "On the Algebra of Logic: A Contribution to the Philosophy of Notation,
5931:
3249:
3159:
3027:
1754:
1055:
1044:
4387:
None of the quantifiers previously discussed apply to a quantification such as
9617:
9264:
9030:
8985:
8980:
7749:
7604:
7575:
7381:
7028:
7022:
6949:
6861:
5951:
5624:
5465:
5442:
5185:
5161:
4382:
902:
326:. They can also be used to define more complex quantifiers, as in the formula
260:
5743:
5703:
5634:
4564:{\displaystyle \exists ^{\mathrm {many} }x_{n}A(x_{1},\ldots ,x_{n-1},x_{n})}
3273:
if it is not within the scope of a quantification for that variable. Thus in
3177:, a single domain of discourse fixed in advance is assumed. For example, in
2313:
As a general rule, swapping two adjacent universal quantifiers with the same
9416:
9234:
9159:
9138:
9068:
9020:
9000:
8901:
8804:
7857:
7774:
7734:
7698:
7634:
7446:
7436:
7409:
7135:
6919:
6903:
6586:
5868:
4802:{\displaystyle \exists ^{\mathrm {few} }x_{n}A(x_{1},\ldots ,x_{n-1},x_{n})}
3086:. Conversely, an existentially quantified formula over an empty range (like
2478:
The existential proposition can be expressed with bounded quantification as
909:
7065:
5323:, and Polish logicians into the 1950s. Most notably, it is the notation of
1857:
For every natural number, its product with 2 equals to its sum with itself.
1742:
Assume a fixed domain of discourse for every quantification, as is done in
6135:
5853:
5718:
Glebskii, Yu. V.; Kogan, D. I.; Liogon'kii, M. I.; Talanov, V. A. (1972).
173:
expresses that everything in the domain satisfies the property denoted by
9329:
9118:
8886:
8684:
8132:
7837:
7431:
7013:
6086:""For all" and "there exists" topical phrases, sentences and expressions"
5493:— a higher-order property used as standard semantics of quantified
5378:
to express "all individuals in the domain of discourse have the property
5256:, was the first to employ a quantifier to bind a variable ranging over a
5150:
Contrary to the other quantifiers, § yields a set rather than a formula.
323:
5719:
5528:
In Quest of
Univeral Logic: A brief overview of formal logic's evolution
2324:
The maximum depth of nesting of quantifiers in a formula is called its "
1923:
This is clearly false; it asserts that there is a single natural number
8482:
7274:
6167:
5735:
5417:
1850:
7172:
2799:" proposition, one needs to show that the predicate is false for all
5272:. Frege's treatment of quantification went largely unremarked until
3540:. Boolean-valued means that the function assumes one of the values
3030:. Expository conventions often reserve some variable names such as "
1076:
1068:
255:
is called a quantified formula. A quantified formula must contain a
5982:. Harvard University Press. The first appearance of quantification.
5980:
From Frege to Gödel: A Source Book on
Mathematical Logic, 1879-1931
5160:
For all but finitely many elements... (sometimes expressed as "for
9194:
8026:
7372:
7217:
5291:
independently invented universal and existential quantifiers, and
5225:(1806–1871) was the first to use "quantifier" in the modern sense.
5217:
265:
5597:
K.R. Apt (1990). "Logic
Programming". In Jan van Leeuwen (ed.).
8934:
7176:
6139:
1217:
Some other quantified expressions are constructed as follows,
392:. Quantifiers have been generalized beginning with the work of
5153:
Some other quantifiers sometimes used in mathematics include:
3548:(interpreted as falsehood). The interpretation of the formula
1026:
36:
5140:{\displaystyle \{n\in \mathbb {N} :n^{2}\leq 4\}=\{0,1,2\}.}
3130:
A more natural way to restrict the domain of discourse uses
6037:
Westerståhl, Dag, 2001, "Quantifiers," in Goble, Lou, ed.,
5660:
Introduction to
Automata Theory, Languages, and Computation
3041:
A universally quantified formula over an empty range (like
5200:
in the 4th century BC, in an account also touching on the
5060:≤ 4 are in {0,1,2}." The same construct is expressible in
4254:
on the set of formulas, by adding, for each free variable
3017:
Every quantification involves one specific variable and a
103:
is an operator that specifies how many individuals in the
5176:
For all elements except those in a set of measure zero...
1080:
1072:
415:
First order quantifiers approximate the meanings of some
270:
Table of truth for
Existential and Universal quantifiers.
1753:
of that variable. This is analogous to the situation in
263:
specifying a property of the referent of that variable.
2940:
is by the amount of quantification. Formulas with less
2409:
This notation is known as restricted or relativized or
60:
3536:
arguments, where each argument ranges over the domain
3075:{\displaystyle \forall x\!\in \!\varnothing \;x\neq x}
5688:. Hochschultext (Springer-Verlag). London: Springer.
5073:
4969:
4842:
4713:
4604:
4472:
4090:
4021:
3936:
3759:
3557:
3467:{\displaystyle \forall x(\exists yB(x,y))\vee C(y,x)}
3406:
3343:{\displaystyle \forall x(\exists yB(x,y))\vee C(y,x)}
3282:
3092:
3047:
2976:
2956:
2919:
2899:
2879:
2856:
2709:
2606:
2540:
2487:
2422:
2365:
2356:, then the universal proposition can be expressed as
2285:, the variables that precede it. In the latter case,
2124:
1970:
1711:
1685:
1655:
1613:
1576:
1542:
1511:
1477:
1442:
1407:
1366:
1332:
1302:
1255:
1226:
1125:
816:
770:
728:
658:
613:
543:
498:
437:
370:
332:
300:
280:
222:
202:
179:
144:
120:
5346:
Peirce's approach to quantification also influenced
5311:. Peirce's notation can be found in the writings of
4250:
Each kind of quantification defines a corresponding
3994:{\displaystyle \exists !x_{n}A(x_{1},\ldots ,x_{n})}
3026:
predicate holds for some natural number or for some
2587:{\displaystyle \exists x\;(x\!\in \!\!D\land P(x)).}
2273:
In the former case, the particular value chosen for
9570:
9455:
9359:
9352:
9147:
9056:
9049:
8968:
8828:
8723:
8555:
8448:
8300:
7993:
7916:
7810:
7714:
7603:
7530:
7465:
7380:
7371:
7293:
7210:
7012:
7000:
6859:
6850:
6759:
6734:
6709:
6633:
6585:
6521:
6496:
6468:
6433:
6383:
6337:
6328:
6266:
6232:
6188:
6179:
5837:
5623:Schwichtenberg, Helmut; Wainer, Stanley S. (2009).
4076:{\displaystyle \exists x_{n}A(x_{1},\ldots ,x_{n})}
3814:{\displaystyle \exists x_{n}A(x_{1},\ldots ,x_{n})}
3612:{\displaystyle \forall x_{n}A(x_{1},\ldots ,x_{n})}
5139:
5037:
4933:
4801:
4689:
4563:
4239:
4075:
3993:
3813:
3611:
3466:
3342:
3120:{\displaystyle \exists x\!\in \!\varnothing \;x=x}
3119:
3074:
2992:
2962:
2925:
2905:
2885:
2865:
2784:
2681:
2586:
2520:
2467:
2398:
2262:
2108:
1727:
1697:
1671:
1635:
1599:
1562:
1528:
1497:
1463:
1428:
1393:
1352:
1318:
1270:
1241:
1181:{\displaystyle \forall {x}{\in }X,(P(x)\lor Q(x))}
1180:
908:The example above is fortunate in that there is a
854:
802:
752:
714:
641:
599:
526:
484:
376:
356:
306:
286:
243:
208:
185:
165:
126:
3103:
3099:
3058:
3054:
2759:
2755:
2726:
2722:
2696:" proposition, one needs no more than to find an
2656:
2652:
2623:
2619:
2559:
2558:
2554:
2498:
2494:
2440:
2436:
2376:
2372:
9427:Segmented discourse representation theory (SDRT)
6016:, Vol. 7, pp. 180–202. Reprinted in Kloesel, N.
5901:Peters, Stanley; Westerståhl, Dag (2006-04-27).
5173:For all elements in a set of positive measure...
5167:There are uncountably many elements such that...
3204:in Zermelo–Fraenkel set theory, one would write
2950:has quantifier elimination if for every formula
2893:" can be viewed as a question "When is there an
2468:{\displaystyle \forall x\;(x\!\in \!D\to P(x)).}
1083:", which stands for "there exists" or "exists".
607:. Dually, the existentially quantified formula
427:Relations to logical conjunction and disjunction
27:Mathematical use of "for all" and "there exists"
5658:John E. Hopcroft and Jeffrey D. Ullman (1979).
5157:There are infinitely many elements such that...
1760:languages, where variables have declared types.
600:{\displaystyle P(a_{1})\land ...\land P(a_{n})}
6276:Affirmative conclusion from a negative premise
4704:otherwise. Similarly, the interpretation of
4321:. As another example, equational axioms, like
3750:. Similarly the interpretation of the formula
2352:) is a predicate dependent on object variable
384:. Other quantifiers are only definable within
364:which expresses that nothing has the property
314:. These quantifiers are standardly defined as
8946:
7188:
6281:Negative conclusion from affirmative premises
6151:
5354:, who invented yet another notation, namely (
4229:
4105:
3248:Mathematical semantics is the application of
2700:for which the predicate is false. Similarly,
715:{\displaystyle P(a_{1})\lor ...\lor P(a_{n})}
8:
5884:(1827); Thoemmes; Facsimile edition (1990)
5131:
5113:
5107:
5074:
5032:
5014:
4922:
4855:
4678:
4611:
3134:. For example, the guarded quantification
747:
735:
479:
444:
5780:, closure makes sense only if the order of
4373:Paucal, multal and other degree quantifiers
893:of propositions. From the point of view of
9356:
9053:
8953:
8939:
8931:
8014:
7609:
7377:
7195:
7181:
7173:
7009:
6856:
6731:
6334:
6185:
6158:
6144:
6136:
6122:Peters, Stanley; Westerståhl, Dag (2002).
6039:The Blackwell Guide to Philosophical Logic
5283:In work that culminated in Peirce (1885),
4217:
4213:
3256:, a mathematical specification of various
3107:
3062:
2763:
2730:
2660:
2627:
2547:
2502:
2429:
2380:
2293:(i.e., it has to be chosen independent of
2180:
2165:
2150:
2137:
2026:
2011:
1998:
1983:
783:
626:
511:
5629:. Cambridge: Cambridge University Press.
5502:— a generalized polyadic quantifier
5423:Around 1895, Peirce began developing his
5095:
5084:
5083:
5072:
4994:
4985:
4984:
4968:
4917:
4893:
4874:
4841:
4790:
4771:
4752:
4736:
4719:
4718:
4712:
4673:
4649:
4630:
4603:
4552:
4533:
4514:
4498:
4478:
4477:
4471:
4228:
4227:
4192:
4173:
4139:
4120:
4104:
4103:
4089:
4064:
4045:
4029:
4020:
3982:
3963:
3947:
3935:
3802:
3783:
3767:
3758:
3600:
3581:
3565:
3556:
3486:assumes as given a domain of individuals
3405:
3281:
3091:
3046:
2981:
2975:
2955:
2918:
2898:
2878:
2855:
2708:
2605:
2539:
2521:{\displaystyle \exists x\!\in \!D\;P(x),}
2486:
2421:
2399:{\displaystyle \forall x\!\in \!D\;P(x).}
2364:
2246:
2208:
2207:
2203:
2192:
2184:
2176:
2175:
2161:
2160:
2123:
2092:
2054:
2053:
2049:
2038:
2030:
2022:
2021:
1994:
1993:
1969:
1786:" might appear after or in the middle of
1778:Informally or in natural language, the "∀
1721:
1710:
1684:
1660:
1654:
1629:
1621:
1617:
1612:
1593:
1585:
1580:
1575:
1556:
1551:
1546:
1541:
1522:
1516:
1510:
1481:
1476:
1441:
1406:
1365:
1339:
1331:
1307:
1301:
1264:
1259:
1254:
1235:
1230:
1225:
1134:
1129:
1124:
846:
827:
815:
794:
769:
727:
703:
669:
657:
612:
588:
554:
542:
497:
473:
451:
436:
369:
331:
299:
279:
221:
201:
178:
143:
119:
83:Learn how and when to remove this message
5784:quantification does not matter, i.e. if
3395:
2692:which shows that to disprove a "for all
5950:Brown, Christopher W. (July 31, 2002).
5517:
3104:
3059:
2838:is a concept of simplification used in
897:, this is immediately a problem, since
803:{\displaystyle \forall x\in B\;x=x^{2}}
274:The most commonly used quantifiers are
5366:for the existential quantification of
5358:) for the universal quantification of
5170:For all but countably many elements...
2850:. Informally, a quantified statement "
983:Algebraic approaches to quantification
9382:Discourse representation theory (DRT)
6046:Numbers, language, and the human mind
5764:
4443:whose interpretation is the function
1600:{\displaystyle \exists {x}{\in }X\,P}
876:using dot notation for multiplication
492:, the universally quantified formula
7:
6094:. From College of Natural Sciences,
4337:, are usually meant to denote their
1429:{\displaystyle \exists x\ \cdot \ P}
855:{\displaystyle 0=0^{2}\land 1=1^{2}}
642:{\displaystyle \exists x\in D\;P(x)}
527:{\displaystyle \forall x\in D\;P(x)}
485:{\displaystyle D=\{a_{1},...a_{n}\}}
9295:Quantificational variability effect
8962:Formal semantics (natural language)
6102:Stanford Encyclopedia of Philosophy
4008:-1 arguments, which is the logical
3373:) is free, while the occurrence of
3240:is the set of all natural numbers.
1907:such that for every natural number
1091:be the set of all Peter's friends,
5686:Introduction to Mathematical Logic
4975:
4849:
4726:
4723:
4720:
4715:
4605:
4488:
4485:
4482:
4479:
4474:
4091:
4022:
3937:
3760:
3558:
3416:
3407:
3292:
3283:
3265:, and an occurrence of a variable
3093:
3048:
2857:
2764:
2749:
2716:
2710:
2661:
2646:
2613:
2607:
2541:
2488:
2423:
2366:
2166:
2151:
2138:
2125:
2012:
1999:
1984:
1971:
1636:{\displaystyle \exists \,x{:}X\,P}
1614:
1577:
1543:
1513:
1478:
1446:
1408:
1370:
1336:
1256:
1227:
1126:
947:A similar analysis applies to the
874:Consider the following statement (
771:
614:
499:
357:{\displaystyle \neg \exists xP(x)}
336:
333:
301:
281:
223:
203:
145:
121:
25:
6000:Grundzüge der theoretischen Logik
5907:. Clarendon Press. pp. 34–.
5904:Quantifiers in Language and Logic
4960:) and read "those". For example,
4427:is a formula with free variables
1563:{\displaystyle \exists {x}{,}\,P}
1394:{\displaystyle (\exists x\ .\ P)}
431:For a finite domain of discourse
412:is the order of quantifications.
8914:
7157:
7156:
6022:Writings of C. S. Peirce, Vol. 5
5995:Principles of Mathematical Logic
5952:"What is Quantifier Elimination"
5445:
4918:
4674:
2827:This section is an excerpt from
1883:, there exists a natural number
404:difference in the definition of
322:, they are interdefinable using
41:
6014:American Journal of Mathematics
5855:Practical Theory of Programming
5838:#Order of quantifiers (nesting)
5038:{\displaystyle \left=\{0,1,2\}}
4989:
2970:, there exists another formula
2942:depth of quantifier alternation
2795:to disprove a "there exists an
1830:For exactly one natural number
1767:of the objects in that domain).
1672:{\displaystyle \bigwedge _{x}P}
1529:{\displaystyle \exists _{x}\,P}
901:rules are expected to generate
9377:Combinatory categorial grammar
6654:Correlation implies causation
6048:. Cambridge University Press.
5662:. Reading/MA: Addison-Wesley.
5327:'s landmark 1930 paper on the
4911:
4867:
4796:
4745:
4667:
4623:
4558:
4507:
4214:
4210:
4166:
4157:
4113:
4070:
4038:
3988:
3956:
3808:
3776:
3606:
3574:
3484:first-order predicate calculus
3461:
3449:
3440:
3437:
3425:
3413:
3337:
3325:
3316:
3313:
3301:
3289:
2776:
2770:
2743:
2740:
2734:
2713:
2673:
2667:
2640:
2637:
2631:
2610:
2578:
2575:
2569:
2548:
2512:
2506:
2459:
2456:
2450:
2444:
2430:
2413:. Equivalently one can write,
2390:
2384:
2257:
2247:
2243:
2231:
2222:
2216:
2209:
2204:
2193:
2185:
2181:
2103:
2093:
2089:
2077:
2068:
2062:
2055:
2050:
2039:
2031:
2027:
1903:There exists a natural number
1865:Order of quantifiers (nesting)
1718:
1712:
1498:{\displaystyle \exists {x}(P)}
1492:
1486:
1458:
1443:
1388:
1367:
1353:{\displaystyle (\exists {x})P}
1344:
1333:
1271:{\displaystyle \forall {x}\,P}
1242:{\displaystyle \exists {x}\,P}
1175:
1172:
1166:
1157:
1151:
1145:
886:This has the appearance of an
709:
696:
675:
662:
636:
630:
594:
581:
560:
547:
521:
515:
351:
345:
238:
232:
160:
154:
1:
9155:Antecedent-contained deletion
8875:History of mathematical logic
6096:University of Hawaii at Manoa
5537:10.13140/RG.2.2.24043.82724/1
5295:. Peirce and Mitchell wrote Π
1860:Some natural number is prime.
1464:{\displaystyle (\exists x:P)}
1319:{\displaystyle \bigvee _{x}P}
959:which can be rephrased using
244:{\displaystyle \exists xP(x)}
166:{\displaystyle \forall xP(x)}
8800:Primitive recursive function
5946:by two first-rate logicians.
5776:in general, for a quantifer
5550:"Predicates and Quantifiers"
4463:then the interpretation of
4399:is divisible by 2 or 3 or 5.
3393:) is bound (i.e. non-free).
3034:" for natural numbers, and "
3000:without quantifiers that is
2993:{\displaystyle \alpha _{QF}}
2941:
2848:theoretical computer science
1934:A less trivial example from
1698:{\displaystyle \bigwedge xP}
1188:, which is read, "for every
870:Infinite domain of discourse
6073:Encyclopedia of Mathematics
5599:Formal Models and Semantics
4012:of the interpretations of
3400:Syntax tree of the formula
3179:Zermelo–Fraenkel set theory
1744:Zermelo–Fraenkel set theory
32:Quantifier (disambiguation)
9680:
9036:Syntax–semantics interface
7864:Schröder–Bernstein theorem
7591:Monadic predicate calculus
7250:Foundations of mathematics
7078:I'm entitled to my opinion
6032:Elements of Symbolic Logic
5998:. Chelsea. Translation of
4415:and cutoff numbers 0 <
4376:
3927:. The interpretation of
3721:for at least one value of
3544:(interpreted as truth) or
2826:
2289:can be a function only of
2277:can be a function of both
1868:
1837:There is one and only one
961:existential quantification
29:
9528:Question under discussion
9478:Conversational scoreboard
9255:Intersective modification
9240:Homogeneity (linguistics)
8910:
8897:Philosophy of mathematics
8846:Automated theorem proving
8017:
7971:Von Neumann–Bernays–Gödel
7612:
7152:
7061:
6934:
6116:"Generalized quantifiers"
6114:Westerståhl, Dag (2005).
6107:Shapiro, Stewart (2000).
5832:). This is satisfied for
5278:Principles of Mathematics
3920:uniqueness quantification
3494:whose free variables are
3185:For every natural number
2866:{\displaystyle \exists x}
1879:For every natural number
1824:uniqueness quantification
1801:For every natural number
987:It is possible to devise
753:{\displaystyle B=\{0,1\}}
193:. On the other hand, the
9588:Distributional semantics
7104:Motte-and-bailey fallacy
6204:Affirming the consequent
5940:Language Proof and Logic
5635:10.1017/cbo9781139031905
5486:Eventually (mathematics)
5335:, and 1931 paper on the
4391:There are many integers
4004:then is the function of
3138:For some natural number
2118:Uniformly continuous if
1964:Pointwise continuous if
1938:regards the concepts of
918:universal quantification
307:{\displaystyle \exists }
287:{\displaystyle \forall }
209:{\displaystyle \exists }
127:{\displaystyle \forall }
55:may need to be rewritten
9583:Computational semantics
9320:Subsective modification
9124:Propositional attitudes
8547:Self-verifying theories
8368:Tarski's axiomatization
7319:Tarski's undefinability
7314:incompleteness theorems
7124:Two wrongs make a right
6455:Denying the correlative
5626:Proofs and Computations
5525:Kashef, Arman. (2023),
5481:Counting quantification
5429:heterogeneous reasoning
4285:is the closed formula ∃
4258:, a quantifier to bind
3832:-1 arguments such that
3630:-1 arguments such that
3353:the occurrence of both
3023:range of quantification
3013:Range of quantification
2963:{\displaystyle \alpha }
2936:One way of classifying
2926:{\displaystyle \ldots }
2886:{\displaystyle \ldots }
421:generalized quantifiers
18:Range of quantification
9613:Philosophy of language
9250:Inalienable possession
9230:Free choice inferences
9225:Faultless disagreement
8996:Generalized quantifier
8921:Mathematics portal
8532:Proof of impossibility
8180:propositional variable
7490:Propositional calculus
7109:Psychologist's fallacy
7046:Argument to moderation
7036:Argument from anecdote
6986:Chronological snobbery
6610:Quoting out of context
6577:Overwhelming exception
6460:Suppressed correlative
6360:Quoting out of context
6235:quantificational logic
6209:Denying the antecedent
5491:Generalized quantifier
5476:Conditional quantifier
5433:diagrammatic inference
5348:William Ernest Johnson
5285:Charles Sanders Peirce
5226:
5141:
5039:
4935:
4803:
4691:
4565:
4241:
4077:
3995:
3815:
3613:
3475:
3468:
3344:
3132:guarded quantification
3121:
3076:
2994:
2964:
2927:
2907:
2887:
2867:
2836:Quantifier elimination
2829:Quantifier elimination
2822:Quantifier elimination
2786:
2683:
2588:
2522:
2469:
2411:bounded quantification
2400:
2332:Equivalent expressions
2264:
2110:
1927:that is the square of
1729:
1728:{\displaystyle (x)\,P}
1699:
1673:
1637:
1601:
1564:
1530:
1499:
1465:
1430:
1395:
1354:
1320:
1272:
1243:
1182:
1012:Charles Sanders Peirce
856:
804:
754:
716:
643:
601:
528:
486:
378:
358:
308:
288:
271:
245:
210:
195:existential quantifier
187:
167:
128:
9508:Plural quantification
9402:Inquisitive semantics
9367:Alternative semantics
8790:Kolmogorov complexity
8743:Computably enumerable
8643:Model complete theory
8435:Principia Mathematica
7495:Propositional formula
7324:Banach–Tarski paradox
7072:The Four Great Errors
7052:Argumentum ad populum
7041:Argument from silence
6745:Argumentum ad baculum
6523:Faulty generalization
6214:Argument from fallacy
5397:Principia Mathematica
5289:Oscar Howard Mitchell
5221:
5142:
5040:
4936:
4804:
4692:
4566:
4319:Fermat's Last Theorem
4242:
4078:
3996:
3816:
3614:
3469:
3399:
3345:
3175:mathematical theories
3122:
3077:
2995:
2965:
2928:
2908:
2888:
2868:
2787:
2684:
2589:
2523:
2470:
2401:
2265:
2111:
1936:mathematical analysis
1849:may be replaced by a
1730:
1700:
1674:
1638:
1602:
1565:
1531:
1500:
1466:
1431:
1396:
1355:
1321:
1273:
1244:
1183:
1107:likes to dance", and
1079:", a rotated letter "
1071:", a rotated letter "
862:, which evaluates to
857:
805:
755:
717:
649:is equivalent to the
644:
602:
534:is equivalent to the
529:
487:
410:(ordinary) continuity
379:
359:
309:
289:
269:
246:
211:
188:
168:
129:
9493:Function application
9300:Responsive predicate
9290:Privative adjectives
8738:Church–Turing thesis
8725:Computability theory
7934:continuum hypothesis
7452:Square of opposition
7310:Gödel's completeness
7090:Invincible ignorance
6896:Reductio ad Stalinum
6882:Reductio ad Hitlerum
6838:Wisdom of repugnance
6605:Moving the goalposts
6470:Illicit transference
6395:Begging the question
6316:Undistributed middle
6224:Mathematical fallacy
6199:Affirming a disjunct
6044:Wiese, Heike, 2003.
5858:, 2nd edition, p. 28
5684:Hans Hermes (1973).
5500:Lindström quantifier
5471:Branching quantifier
5303:where we now write ∀
5071:
5062:set-builder notation
4967:
4840:
4711:
4602:
4470:
4395:< 100, such that
4088:
4019:
3934:
3757:
3555:
3508:is interpreted as a
3404:
3280:
3090:
3045:
2974:
2954:
2917:
2897:
2877:
2854:
2812:logically equivalent
2707:
2604:
2538:
2485:
2420:
2363:
2122:
1968:
1758:computer programming
1709:
1683:
1653:
1611:
1574:
1540:
1509:
1475:
1440:
1405:
1364:
1330:
1300:
1253:
1224:
1192:that is a member of
1123:
1024:axiomatic set theory
814:
768:
726:
656:
611:
541:
496:
435:
368:
330:
298:
278:
220:
200:
177:
142:
118:
113:universal quantifier
111:. For instance, the
30:For other uses, see
9659:Philosophical logic
9578:Cognitive semantics
9543:Strawson entailment
9488:Existential closure
9432:Situation semantics
9335:Temperature paradox
9305:Rising declaratives
9270:Modal subordination
9245:Hurford disjunction
9205:Discourse relations
8892:Mathematical object
8783:P versus NP problem
8748:Computable function
8542:Reverse mathematics
8468:Logical consequence
8345:primitive recursive
8340:elementary function
8113:Free/bound variable
7966:Tarski–Grothendieck
7485:Logical connectives
7415:Logical equivalence
7265:Logical consequence
6823:Parade of horribles
6799:In-group favoritism
6625:Syntactic ambiguity
6268:Syllogistic fallacy
6191:propositional logic
5976:Jean van Heijenoort
5808:) is equivalent to
5461:Absolute generality
5258:domain of discourse
4812:is the function of
4574:is the function of
4409:probability measure
4264:existential closure
4262:. For example, the
3127:) is always false.
3019:domain of discourse
2810:, every formula is
1010:, and developed by
722:. For example, if
651:logical disjunction
536:logical conjunction
390:higher order logics
105:domain of discourse
9654:Quantifier (logic)
9623:Semantics of logic
9548:Strict conditional
9518:Quantifier raising
9483:Downward entailing
9463:Autonomy of syntax
9392:Generative grammar
9372:Categorial grammar
9310:Scalar implicature
9215:Epistemic modality
9190:De dicto and de re
8690:Transfer principle
8653:Semantics of logic
8638:Categorical theory
8614:Non-standard model
8128:Logical connective
7255:Information theory
7204:Mathematical logic
6909:Poisoning the well
6726:Proof by assertion
6701:Texas sharpshooter
6635:Questionable cause
6572:Slothful induction
6531:Anecdotal evidence
6391:Circular reasoning
6286:Exclusive premises
6248:Illicit conversion
6129:2012-07-16 at the
5990:Ackermann, Wilhelm
5850:Hehner, Eric C. R.
5736:10.1007/bf01071084
5425:existential graphs
5317:Leopold Loewenheim
5234:Augustus De Morgan
5227:
5223:Augustus De Morgan
5202:alethic modalities
5137:
5035:
4931:
4799:
4687:
4561:
4407:, we have given a
4237:
4073:
3991:
3918:The semantics for
3811:
3609:
3476:
3464:
3340:
3117:
3072:
2990:
2960:
2923:
2903:
2883:
2863:
2840:mathematical logic
2816:prenex normal form
2782:
2679:
2584:
2518:
2465:
2396:
2260:
2106:
1725:
1695:
1669:
1665:
1633:
1597:
1560:
1526:
1495:
1461:
1426:
1391:
1350:
1316:
1312:
1268:
1239:
1178:
1008:Augustus De Morgan
852:
800:
750:
712:
639:
597:
524:
482:
406:uniform continuity
386:second order logic
374:
354:
304:
284:
272:
241:
206:
183:
163:
124:
9631:
9630:
9603:Logic translation
9566:
9565:
9558:Universal grinder
9538:Squiggle operator
9498:Meaning postulate
9437:Supervaluationism
9407:Intensional logic
9387:Dynamic semantics
9348:
9347:
9180:Crossover effects
9129:Tense–aspect–mood
9109:Lexical semantics
8928:
8927:
8860:Abstract category
8663:Theories of truth
8473:Rule of inference
8463:Natural deduction
8444:
8443:
7989:
7988:
7694:Cartesian product
7599:
7598:
7505:Many-valued logic
7480:Boolean functions
7363:Russell's paradox
7338:diagonal argument
7235:First-order logic
7170:
7169:
7148:
7147:
7144:
7143:
7084:Ignoratio elenchi
6996:
6995:
6846:
6845:
6808:Not invented here
6513:Converse accident
6435:Correlative-based
6412:Compound question
6355:False attribution
6350:False equivalence
6324:
6323:
6109:"Classical Logic"
6092:on March 1, 2000.
6028:Reichenbach, Hans
6004:first-order logic
5944:first-order logic
5914:978-0-19-929125-0
5708:Here: Def. II.1.5
5644:978-1-139-03190-5
5574:"1.2 Quantifiers"
5453:Philosophy portal
5333:first-order logic
5260:and appearing in
5244:as quantifiers".
4952:Other quantifiers
4339:universal closure
3886:for at least one
3512:-valued function
2906:{\displaystyle x}
1815:For at least one
1656:
1422:
1416:
1384:
1378:
1303:
1115:) the predicate "
1037:Cylindric algebra
989:abstract algebras
914:irrational number
377:{\displaystyle P}
186:{\displaystyle P}
93:
92:
85:
65:lead layout guide
16:(Redirected from
9671:
9608:Linguistics wars
9533:Semantic parsing
9422:Montague grammar
9357:
9200:Deontic modality
9054:
9041:Truth conditions
8976:Compositionality
8969:Central concepts
8955:
8948:
8941:
8932:
8919:
8918:
8870:History of logic
8865:Category of sets
8758:Decision problem
8537:Ordinal analysis
8478:Sequent calculus
8376:Boolean algebras
8316:
8315:
8290:
8261:logical/constant
8015:
8001:
7924:Zermelo–Fraenkel
7675:Set operations:
7610:
7547:
7378:
7358:Löwenheim–Skolem
7245:Formal semantics
7197:
7190:
7183:
7174:
7160:
7159:
7131:Special pleading
7010:
6871:Appeal to motive
6857:
6833:Stirring symbols
6813:Island mentality
6751:Wishful thinking
6732:
6448:Perfect solution
6425:No true Scotsman
6420:Complex question
6405:Leading question
6384:Question-begging
6370:No true Scotsman
6335:
6258:Quantifier shift
6253:Proof by example
6186:
6160:
6153:
6146:
6137:
6093:
6088:. Archived from
6081:
5974:. Translated in
5962:
5960:
5958:
5936:Etchemendy, John
5919:
5918:
5898:
5892:
5880:George Bentham,
5878:
5872:
5865:
5859:
5847:
5841:
5774:
5768:
5762:
5756:
5755:
5715:
5709:
5707:
5681:
5675:
5673:
5655:
5649:
5648:
5620:
5614:
5612:
5594:
5588:
5587:
5585:
5584:
5570:
5564:
5563:
5561:
5560:
5554:www.csm.ornl.gov
5546:
5540:
5539:
5522:
5506:Quantifier shift
5455:
5450:
5449:
5448:
5341:Peano arithmetic
5287:and his student
5274:Bertrand Russell
5230:William Hamilton
5146:
5144:
5143:
5138:
5100:
5099:
5087:
5044:
5042:
5041:
5036:
5010:
5006:
4999:
4998:
4988:
4940:
4938:
4937:
4932:
4921:
4904:
4903:
4879:
4878:
4808:
4806:
4805:
4800:
4795:
4794:
4782:
4781:
4757:
4756:
4741:
4740:
4731:
4730:
4729:
4696:
4694:
4693:
4688:
4677:
4660:
4659:
4635:
4634:
4570:
4568:
4567:
4562:
4557:
4556:
4544:
4543:
4519:
4518:
4503:
4502:
4493:
4492:
4491:
4379:Fubini's theorem
4252:closure operator
4246:
4244:
4243:
4238:
4233:
4232:
4203:
4202:
4178:
4177:
4150:
4149:
4125:
4124:
4109:
4108:
4082:
4080:
4079:
4074:
4069:
4068:
4050:
4049:
4034:
4033:
4000:
3998:
3997:
3992:
3987:
3986:
3968:
3967:
3952:
3951:
3824:is the function
3820:
3818:
3817:
3812:
3807:
3806:
3788:
3787:
3772:
3771:
3622:is the function
3618:
3616:
3615:
3610:
3605:
3604:
3586:
3585:
3570:
3569:
3473:
3471:
3470:
3465:
3349:
3347:
3346:
3341:
3258:semantic domains
3244:Formal semantics
3126:
3124:
3123:
3118:
3081:
3079:
3078:
3073:
2999:
2997:
2996:
2991:
2989:
2988:
2969:
2967:
2966:
2961:
2932:
2930:
2929:
2924:
2912:
2910:
2909:
2904:
2892:
2890:
2889:
2884:
2872:
2870:
2869:
2864:
2814:to a formula in
2791:
2789:
2788:
2783:
2688:
2686:
2685:
2680:
2593:
2591:
2590:
2585:
2531:or equivalently
2527:
2525:
2524:
2519:
2474:
2472:
2471:
2466:
2405:
2403:
2402:
2397:
2297:). For example,
2269:
2267:
2266:
2261:
2250:
2212:
2196:
2188:
2179:
2164:
2115:
2113:
2112:
2107:
2096:
2058:
2042:
2034:
2025:
1997:
1871:Quantifier shift
1853:. For example,
1808:There exists an
1773:variable capture
1755:statically typed
1734:
1732:
1731:
1726:
1704:
1702:
1701:
1696:
1678:
1676:
1675:
1670:
1664:
1642:
1640:
1639:
1634:
1625:
1606:
1604:
1603:
1598:
1589:
1584:
1569:
1567:
1566:
1561:
1555:
1550:
1535:
1533:
1532:
1527:
1521:
1520:
1504:
1502:
1501:
1496:
1485:
1470:
1468:
1467:
1462:
1435:
1433:
1432:
1427:
1420:
1414:
1400:
1398:
1397:
1392:
1382:
1376:
1359:
1357:
1356:
1351:
1343:
1325:
1323:
1322:
1317:
1311:
1289:and set members
1277:
1275:
1274:
1269:
1263:
1248:
1246:
1245:
1240:
1234:
1187:
1185:
1184:
1179:
1138:
1133:
1052:polyadic algebra
1031:Peano arithmetic
1004:Relation algebra
997:formal languages
978:is equal to 5+5.
895:formal languages
861:
859:
858:
853:
851:
850:
832:
831:
809:
807:
806:
801:
799:
798:
759:
757:
756:
751:
721:
719:
718:
713:
708:
707:
674:
673:
648:
646:
645:
640:
606:
604:
603:
598:
593:
592:
559:
558:
533:
531:
530:
525:
491:
489:
488:
483:
478:
477:
456:
455:
417:natural language
383:
381:
380:
375:
363:
361:
360:
355:
313:
311:
310:
305:
293:
291:
290:
285:
250:
248:
247:
242:
215:
213:
212:
207:
192:
190:
189:
184:
172:
170:
169:
164:
133:
131:
130:
125:
88:
81:
77:
74:
68:
61:improve the lead
45:
44:
37:
21:
9679:
9678:
9674:
9673:
9672:
9670:
9669:
9668:
9649:Predicate logic
9634:
9633:
9632:
9627:
9562:
9451:
9412:Lambda calculus
9344:
9315:Sloppy identity
9275:Opaque contexts
9210:Donkey anaphora
9175:Counterfactuals
9143:
9045:
8964:
8959:
8929:
8924:
8913:
8906:
8851:Category theory
8841:Algebraic logic
8824:
8795:Lambda calculus
8733:Church encoding
8719:
8695:Truth predicate
8551:
8517:Complete theory
8440:
8309:
8305:
8301:
8296:
8288:
8008: and
8004:
7999:
7985:
7961:New Foundations
7929:axiom of choice
7912:
7874:Gödel numbering
7814: and
7806:
7710:
7595:
7545:
7526:
7475:Boolean algebra
7461:
7425:Equiconsistency
7390:Classical logic
7367:
7348:Halting problem
7336: and
7312: and
7300: and
7299:
7294:Theorems (
7289:
7206:
7201:
7171:
7166:
7140:
7114:Rationalization
7057:
7004:
6992:
6930:
6852:Genetic fallacy
6842:
6755:
6730:
6705:
6629:
6620:Sorites paradox
6600:False precision
6581:
6562:Double counting
6517:
6492:
6464:
6429:
6416:Loaded question
6400:Loaded language
6379:
6320:
6262:
6228:
6175:
6164:
6131:Wayback Machine
6084:
6066:
6063:
6030:, 1975 (1947).
5992:, 1950 (1928).
5971:Begriffsschrift
5956:
5954:
5949:
5928:
5923:
5922:
5915:
5900:
5899:
5895:
5879:
5875:
5866:
5862:
5848:
5844:
5775:
5771:
5763:
5759:
5717:
5716:
5712:
5696:
5683:
5682:
5678:
5670:
5657:
5656:
5652:
5645:
5622:
5621:
5617:
5609:
5596:
5595:
5591:
5582:
5580:
5578:www.whitman.edu
5572:
5571:
5567:
5558:
5556:
5548:
5547:
5543:
5524:
5523:
5519:
5514:
5451:
5446:
5444:
5441:
5362:and (in 1897) ∃
5302:
5298:
5293:bound variables
5253:Begriffsschrift
5183:
5091:
5069:
5068:
5048:is read "those
4990:
4974:
4970:
4965:
4964:
4954:
4889:
4870:
4838:
4837:
4833:if and only if
4828:
4818:
4786:
4767:
4748:
4732:
4714:
4709:
4708:
4645:
4626:
4600:
4599:
4595:if and only if
4590:
4580:
4548:
4529:
4510:
4494:
4473:
4468:
4467:
4462:
4453:
4442:
4433:
4385:
4375:
4188:
4169:
4135:
4116:
4086:
4085:
4060:
4041:
4025:
4017:
4016:
3978:
3959:
3943:
3932:
3931:
3910:
3900:
3877:
3867:
3857:if and only if
3852:
3842:
3798:
3779:
3763:
3755:
3754:
3745:
3735:
3712:
3702:
3675:
3665:
3655:if and only if
3650:
3640:
3596:
3577:
3561:
3553:
3552:
3531:
3522:
3507:
3500:
3402:
3401:
3278:
3277:
3246:
3088:
3087:
3043:
3042:
3015:
3010:
3009:
2977:
2972:
2971:
2952:
2951:
2915:
2914:
2895:
2894:
2875:
2874:
2852:
2851:
2832:
2824:
2808:classical logic
2705:
2704:
2602:
2601:
2536:
2535:
2483:
2482:
2418:
2417:
2361:
2360:
2340:is a domain of
2334:
2326:quantifier rank
2120:
2119:
1966:
1965:
1873:
1867:
1707:
1706:
1681:
1680:
1651:
1650:
1609:
1608:
1572:
1571:
1538:
1537:
1512:
1507:
1506:
1473:
1472:
1438:
1437:
1403:
1402:
1362:
1361:
1328:
1327:
1298:
1297:
1251:
1250:
1222:
1221:
1121:
1120:
1065:
985:
872:
842:
823:
812:
811:
790:
766:
765:
724:
723:
699:
665:
654:
653:
609:
608:
584:
550:
539:
538:
494:
493:
469:
447:
433:
432:
429:
366:
365:
328:
327:
320:classical logic
296:
295:
276:
275:
218:
217:
216:in the formula
198:
197:
175:
174:
140:
139:
116:
115:
89:
78:
72:
69:
58:
46:
42:
35:
28:
23:
22:
15:
12:
11:
5:
9677:
9675:
9667:
9666:
9661:
9656:
9651:
9646:
9636:
9635:
9629:
9628:
9626:
9625:
9620:
9615:
9610:
9605:
9600:
9598:Inferentialism
9595:
9593:Formal grammar
9590:
9585:
9580:
9574:
9572:
9568:
9567:
9564:
9563:
9561:
9560:
9555:
9550:
9545:
9540:
9535:
9530:
9525:
9520:
9515:
9513:Possible world
9510:
9505:
9500:
9495:
9490:
9485:
9480:
9475:
9470:
9465:
9459:
9457:
9453:
9452:
9450:
9449:
9444:
9439:
9434:
9429:
9424:
9419:
9414:
9409:
9404:
9399:
9397:Glue semantics
9394:
9389:
9384:
9379:
9374:
9369:
9363:
9361:
9360:Formal systems
9354:
9350:
9349:
9346:
9345:
9343:
9342:
9337:
9332:
9327:
9322:
9317:
9312:
9307:
9302:
9297:
9292:
9287:
9285:Polarity items
9282:
9277:
9272:
9267:
9262:
9257:
9252:
9247:
9242:
9237:
9232:
9227:
9222:
9217:
9212:
9207:
9202:
9197:
9192:
9187:
9182:
9177:
9172:
9170:Conservativity
9167:
9162:
9157:
9151:
9149:
9145:
9144:
9142:
9141:
9136:
9134:Quantification
9131:
9126:
9121:
9116:
9111:
9106:
9101:
9096:
9091:
9086:
9081:
9076:
9071:
9066:
9060:
9058:
9051:
9047:
9046:
9044:
9043:
9038:
9033:
9028:
9023:
9018:
9013:
9011:Presupposition
9008:
9003:
8998:
8993:
8988:
8983:
8978:
8972:
8970:
8966:
8965:
8960:
8958:
8957:
8950:
8943:
8935:
8926:
8925:
8911:
8908:
8907:
8905:
8904:
8899:
8894:
8889:
8884:
8883:
8882:
8872:
8867:
8862:
8853:
8848:
8843:
8838:
8836:Abstract logic
8832:
8830:
8826:
8825:
8823:
8822:
8817:
8815:Turing machine
8812:
8807:
8802:
8797:
8792:
8787:
8786:
8785:
8780:
8775:
8770:
8765:
8755:
8753:Computable set
8750:
8745:
8740:
8735:
8729:
8727:
8721:
8720:
8718:
8717:
8712:
8707:
8702:
8697:
8692:
8687:
8682:
8681:
8680:
8675:
8670:
8660:
8655:
8650:
8648:Satisfiability
8645:
8640:
8635:
8634:
8633:
8623:
8622:
8621:
8611:
8610:
8609:
8604:
8599:
8594:
8589:
8579:
8578:
8577:
8572:
8565:Interpretation
8561:
8559:
8553:
8552:
8550:
8549:
8544:
8539:
8534:
8529:
8519:
8514:
8513:
8512:
8511:
8510:
8500:
8495:
8485:
8480:
8475:
8470:
8465:
8460:
8454:
8452:
8446:
8445:
8442:
8441:
8439:
8438:
8430:
8429:
8428:
8427:
8422:
8421:
8420:
8415:
8410:
8390:
8389:
8388:
8386:minimal axioms
8383:
8372:
8371:
8370:
8359:
8358:
8357:
8352:
8347:
8342:
8337:
8332:
8319:
8317:
8298:
8297:
8295:
8294:
8293:
8292:
8280:
8275:
8274:
8273:
8268:
8263:
8258:
8248:
8243:
8238:
8233:
8232:
8231:
8226:
8216:
8215:
8214:
8209:
8204:
8199:
8189:
8184:
8183:
8182:
8177:
8172:
8162:
8161:
8160:
8155:
8150:
8145:
8140:
8135:
8125:
8120:
8115:
8110:
8109:
8108:
8103:
8098:
8093:
8083:
8078:
8076:Formation rule
8073:
8068:
8067:
8066:
8061:
8051:
8050:
8049:
8039:
8034:
8029:
8024:
8018:
8012:
7995:Formal systems
7991:
7990:
7987:
7986:
7984:
7983:
7978:
7973:
7968:
7963:
7958:
7953:
7948:
7943:
7938:
7937:
7936:
7931:
7920:
7918:
7914:
7913:
7911:
7910:
7909:
7908:
7898:
7893:
7892:
7891:
7884:Large cardinal
7881:
7876:
7871:
7866:
7861:
7847:
7846:
7845:
7840:
7835:
7820:
7818:
7808:
7807:
7805:
7804:
7803:
7802:
7797:
7792:
7782:
7777:
7772:
7767:
7762:
7757:
7752:
7747:
7742:
7737:
7732:
7727:
7721:
7719:
7712:
7711:
7709:
7708:
7707:
7706:
7701:
7696:
7691:
7686:
7681:
7673:
7672:
7671:
7666:
7656:
7651:
7649:Extensionality
7646:
7644:Ordinal number
7641:
7631:
7626:
7625:
7624:
7613:
7607:
7601:
7600:
7597:
7596:
7594:
7593:
7588:
7583:
7578:
7573:
7568:
7563:
7562:
7561:
7551:
7550:
7549:
7536:
7534:
7528:
7527:
7525:
7524:
7523:
7522:
7517:
7512:
7502:
7497:
7492:
7487:
7482:
7477:
7471:
7469:
7463:
7462:
7460:
7459:
7454:
7449:
7444:
7439:
7434:
7429:
7428:
7427:
7417:
7412:
7407:
7402:
7397:
7392:
7386:
7384:
7375:
7369:
7368:
7366:
7365:
7360:
7355:
7350:
7345:
7340:
7328:Cantor's
7326:
7321:
7316:
7306:
7304:
7291:
7290:
7288:
7287:
7282:
7277:
7272:
7267:
7262:
7257:
7252:
7247:
7242:
7237:
7232:
7227:
7226:
7225:
7214:
7212:
7208:
7207:
7202:
7200:
7199:
7192:
7185:
7177:
7168:
7167:
7165:
7164:
7153:
7150:
7149:
7146:
7145:
7142:
7141:
7139:
7138:
7133:
7128:
7127:
7126:
7116:
7111:
7106:
7101:
7092:
7087:
7080:
7075:
7068:
7062:
7059:
7058:
7056:
7055:
7048:
7043:
7038:
7033:
7032:
7031:
7018:
7016:
7007:
6998:
6997:
6994:
6993:
6991:
6990:
6989:
6988:
6974:
6969:
6964:
6963:
6962:
6953:
6946:
6944:Accomplishment
6935:
6932:
6931:
6929:
6928:
6923:
6916:
6911:
6906:
6901:
6900:
6899:
6892:
6891:
6890:
6873:
6867:
6865:
6854:
6848:
6847:
6844:
6843:
6841:
6840:
6835:
6830:
6825:
6820:
6815:
6810:
6801:
6796:
6791:
6786:
6781:
6776:
6771:
6765:
6763:
6757:
6756:
6754:
6753:
6748:
6740:
6738:
6729:
6728:
6719:
6713:
6711:
6707:
6706:
6704:
6703:
6698:
6696:Slippery slope
6693:
6688:
6683:
6682:
6681:
6671:
6670:
6669:
6662:
6652:
6651:
6650:
6639:
6637:
6631:
6630:
6628:
6627:
6622:
6617:
6615:Slippery slope
6612:
6607:
6602:
6597:
6591:
6589:
6583:
6582:
6580:
6579:
6574:
6569:
6564:
6559:
6550:
6549:
6548:
6543:
6541:Cherry picking
6533:
6527:
6525:
6519:
6518:
6516:
6515:
6510:
6504:
6502:
6494:
6493:
6491:
6490:
6485:
6480:
6474:
6472:
6466:
6465:
6463:
6462:
6457:
6452:
6451:
6450:
6439:
6437:
6431:
6430:
6428:
6427:
6422:
6409:
6408:
6407:
6397:
6387:
6385:
6381:
6380:
6378:
6377:
6372:
6367:
6362:
6357:
6352:
6347:
6341:
6339:
6332:
6326:
6325:
6322:
6321:
6319:
6318:
6313:
6308:
6303:
6298:
6293:
6288:
6283:
6278:
6272:
6270:
6264:
6263:
6261:
6260:
6255:
6250:
6245:
6239:
6237:
6230:
6229:
6227:
6226:
6221:
6216:
6211:
6206:
6201:
6195:
6193:
6183:
6177:
6176:
6165:
6163:
6162:
6155:
6148:
6140:
6134:
6133:
6120:
6119:
6118:
6112:
6099:
6082:
6062:
6061:External links
6059:
6058:
6057:
6042:
6035:
6025:
6020:, eds., 1993.
6007:
5986:Hilbert, David
5983:
5966:Frege, Gottlob
5963:
5947:
5927:
5924:
5921:
5920:
5913:
5893:
5873:
5860:
5842:
5769:
5757:
5730:(2): 142–154.
5710:
5694:
5676:
5668:
5650:
5643:
5615:
5607:
5589:
5565:
5541:
5516:
5515:
5513:
5510:
5509:
5508:
5503:
5497:
5488:
5483:
5478:
5473:
5468:
5463:
5457:
5456:
5440:
5437:
5352:Giuseppe Peano
5337:incompleteness
5321:Thoralf Skolem
5313:Ernst Schröder
5300:
5296:
5270:contraposition
5250:, in his 1879
5211:published his
5209:George Bentham
5182:
5179:
5178:
5177:
5174:
5171:
5168:
5165:
5164:elements...").
5158:
5148:
5147:
5136:
5133:
5130:
5127:
5124:
5121:
5118:
5115:
5112:
5109:
5106:
5103:
5098:
5094:
5090:
5086:
5082:
5079:
5076:
5046:
5045:
5034:
5031:
5028:
5025:
5022:
5019:
5016:
5013:
5009:
5005:
5002:
4997:
4993:
4987:
4983:
4980:
4977:
4973:
4953:
4950:
4942:
4941:
4930:
4927:
4924:
4920:
4916:
4913:
4910:
4907:
4902:
4899:
4896:
4892:
4888:
4885:
4882:
4877:
4873:
4869:
4866:
4863:
4860:
4857:
4854:
4851:
4848:
4845:
4823:
4816:
4810:
4809:
4798:
4793:
4789:
4785:
4780:
4777:
4774:
4770:
4766:
4763:
4760:
4755:
4751:
4747:
4744:
4739:
4735:
4728:
4725:
4722:
4717:
4698:
4697:
4686:
4683:
4680:
4676:
4672:
4669:
4666:
4663:
4658:
4655:
4652:
4648:
4644:
4641:
4638:
4633:
4629:
4625:
4622:
4619:
4616:
4613:
4610:
4607:
4585:
4578:
4572:
4571:
4560:
4555:
4551:
4547:
4542:
4539:
4536:
4532:
4528:
4525:
4522:
4517:
4513:
4509:
4506:
4501:
4497:
4490:
4487:
4484:
4481:
4476:
4458:
4451:
4438:
4431:
4401:
4400:
4374:
4371:
4248:
4247:
4236:
4231:
4226:
4223:
4220:
4216:
4212:
4209:
4206:
4201:
4198:
4195:
4191:
4187:
4184:
4181:
4176:
4172:
4168:
4165:
4162:
4159:
4156:
4153:
4148:
4145:
4142:
4138:
4134:
4131:
4128:
4123:
4119:
4115:
4112:
4107:
4102:
4099:
4096:
4093:
4083:
4072:
4067:
4063:
4059:
4056:
4053:
4048:
4044:
4040:
4037:
4032:
4028:
4024:
4002:
4001:
3990:
3985:
3981:
3977:
3974:
3971:
3966:
3962:
3958:
3955:
3950:
3946:
3942:
3939:
3905:
3898:
3872:
3865:
3847:
3840:
3822:
3821:
3810:
3805:
3801:
3797:
3794:
3791:
3786:
3782:
3778:
3775:
3770:
3766:
3762:
3740:
3733:
3707:
3700:
3670:
3663:
3645:
3638:
3620:
3619:
3608:
3603:
3599:
3595:
3592:
3589:
3584:
3580:
3576:
3573:
3568:
3564:
3560:
3527:
3520:
3505:
3498:
3480:interpretation
3463:
3460:
3457:
3454:
3451:
3448:
3445:
3442:
3439:
3436:
3433:
3430:
3427:
3424:
3421:
3418:
3415:
3412:
3409:
3351:
3350:
3339:
3336:
3333:
3330:
3327:
3324:
3321:
3318:
3315:
3312:
3309:
3306:
3303:
3300:
3297:
3294:
3291:
3288:
3285:
3245:
3242:
3234:
3233:
3202:
3201:
3171:
3170:
3152:
3151:
3116:
3113:
3110:
3106:
3102:
3098:
3095:
3084:vacuously true
3071:
3068:
3065:
3061:
3057:
3053:
3050:
3014:
3011:
2987:
2984:
2980:
2959:
2922:
2902:
2882:
2862:
2859:
2833:
2825:
2823:
2820:
2793:
2792:
2781:
2778:
2775:
2772:
2769:
2766:
2762:
2758:
2754:
2751:
2748:
2745:
2742:
2739:
2736:
2733:
2729:
2725:
2721:
2718:
2715:
2712:
2690:
2689:
2678:
2675:
2672:
2669:
2666:
2663:
2659:
2655:
2651:
2648:
2645:
2642:
2639:
2636:
2633:
2630:
2626:
2622:
2618:
2615:
2612:
2609:
2595:
2594:
2583:
2580:
2577:
2574:
2571:
2568:
2565:
2562:
2557:
2553:
2550:
2546:
2543:
2529:
2528:
2517:
2514:
2511:
2508:
2505:
2501:
2497:
2493:
2490:
2476:
2475:
2464:
2461:
2458:
2455:
2452:
2449:
2446:
2443:
2439:
2435:
2432:
2428:
2425:
2407:
2406:
2395:
2392:
2389:
2386:
2383:
2379:
2375:
2371:
2368:
2333:
2330:
2271:
2270:
2259:
2256:
2253:
2249:
2245:
2242:
2239:
2236:
2233:
2230:
2227:
2224:
2221:
2218:
2215:
2211:
2206:
2202:
2199:
2195:
2191:
2187:
2183:
2178:
2174:
2171:
2168:
2163:
2159:
2156:
2153:
2149:
2146:
2143:
2140:
2136:
2133:
2130:
2127:
2116:
2105:
2102:
2099:
2095:
2091:
2088:
2085:
2082:
2079:
2076:
2073:
2070:
2067:
2064:
2061:
2057:
2052:
2048:
2045:
2041:
2037:
2033:
2029:
2024:
2020:
2017:
2014:
2010:
2007:
2004:
2001:
1996:
1992:
1989:
1986:
1982:
1979:
1976:
1973:
1921:
1920:
1897:
1896:
1866:
1863:
1862:
1861:
1858:
1843:
1842:
1841:such that ....
1835:
1820:
1819:
1813:
1806:
1769:
1768:
1761:
1747:
1736:
1735:
1724:
1720:
1717:
1714:
1705:
1694:
1691:
1688:
1679:
1668:
1663:
1659:
1644:
1643:
1632:
1628:
1624:
1620:
1616:
1607:
1596:
1592:
1588:
1583:
1579:
1570:
1559:
1554:
1549:
1545:
1536:
1525:
1519:
1515:
1505:
1494:
1491:
1488:
1484:
1480:
1471:
1460:
1457:
1454:
1451:
1448:
1445:
1436:
1425:
1419:
1413:
1410:
1401:
1390:
1387:
1381:
1375:
1372:
1369:
1360:
1349:
1346:
1342:
1338:
1335:
1326:
1315:
1310:
1306:
1281:for a formula
1279:
1278:
1267:
1262:
1258:
1249:
1238:
1233:
1229:
1177:
1174:
1171:
1168:
1165:
1162:
1159:
1156:
1153:
1150:
1147:
1144:
1141:
1137:
1132:
1128:
1064:
1061:
1060:
1059:
1048:
1034:
1016:Ernst Schröder
1006:, invented by
984:
981:
980:
979:
969:natural number
957:
956:
945:
944:
926:natural number
884:
883:
871:
868:
849:
845:
841:
838:
835:
830:
826:
822:
819:
797:
793:
789:
786:
782:
779:
776:
773:
764:, the formula
760:is the set of
749:
746:
743:
740:
737:
734:
731:
711:
706:
702:
698:
695:
692:
689:
686:
683:
680:
677:
672:
668:
664:
661:
638:
635:
632:
629:
625:
622:
619:
616:
596:
591:
587:
583:
580:
577:
574:
571:
568:
565:
562:
557:
553:
549:
546:
523:
520:
517:
514:
510:
507:
504:
501:
481:
476:
472:
468:
465:
462:
459:
454:
450:
446:
443:
440:
428:
425:
373:
353:
350:
347:
344:
341:
338:
335:
303:
283:
257:bound variable
240:
237:
234:
231:
228:
225:
205:
182:
162:
159:
156:
153:
150:
147:
123:
91:
90:
50:The article's
49:
47:
40:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
9676:
9665:
9662:
9660:
9657:
9655:
9652:
9650:
9647:
9645:
9642:
9641:
9639:
9624:
9621:
9619:
9616:
9614:
9611:
9609:
9606:
9604:
9601:
9599:
9596:
9594:
9591:
9589:
9586:
9584:
9581:
9579:
9576:
9575:
9573:
9569:
9559:
9556:
9554:
9551:
9549:
9546:
9544:
9541:
9539:
9536:
9534:
9531:
9529:
9526:
9524:
9521:
9519:
9516:
9514:
9511:
9509:
9506:
9504:
9501:
9499:
9496:
9494:
9491:
9489:
9486:
9484:
9481:
9479:
9476:
9474:
9471:
9469:
9466:
9464:
9461:
9460:
9458:
9454:
9448:
9445:
9443:
9440:
9438:
9435:
9433:
9430:
9428:
9425:
9423:
9420:
9418:
9415:
9413:
9410:
9408:
9405:
9403:
9400:
9398:
9395:
9393:
9390:
9388:
9385:
9383:
9380:
9378:
9375:
9373:
9370:
9368:
9365:
9364:
9362:
9358:
9355:
9351:
9341:
9338:
9336:
9333:
9331:
9328:
9326:
9323:
9321:
9318:
9316:
9313:
9311:
9308:
9306:
9303:
9301:
9298:
9296:
9293:
9291:
9288:
9286:
9283:
9281:
9280:Performatives
9278:
9276:
9273:
9271:
9268:
9266:
9263:
9261:
9260:Logophoricity
9258:
9256:
9253:
9251:
9248:
9246:
9243:
9241:
9238:
9236:
9233:
9231:
9228:
9226:
9223:
9221:
9218:
9216:
9213:
9211:
9208:
9206:
9203:
9201:
9198:
9196:
9193:
9191:
9188:
9186:
9183:
9181:
9178:
9176:
9173:
9171:
9168:
9166:
9163:
9161:
9158:
9156:
9153:
9152:
9150:
9146:
9140:
9137:
9135:
9132:
9130:
9127:
9125:
9122:
9120:
9117:
9115:
9112:
9110:
9107:
9105:
9102:
9100:
9097:
9095:
9094:Evidentiality
9092:
9090:
9087:
9085:
9082:
9080:
9077:
9075:
9072:
9070:
9067:
9065:
9062:
9061:
9059:
9055:
9052:
9048:
9042:
9039:
9037:
9034:
9032:
9029:
9027:
9024:
9022:
9019:
9017:
9014:
9012:
9009:
9007:
9004:
9002:
8999:
8997:
8994:
8992:
8989:
8987:
8984:
8982:
8979:
8977:
8974:
8973:
8971:
8967:
8963:
8956:
8951:
8949:
8944:
8942:
8937:
8936:
8933:
8923:
8922:
8917:
8909:
8903:
8900:
8898:
8895:
8893:
8890:
8888:
8885:
8881:
8878:
8877:
8876:
8873:
8871:
8868:
8866:
8863:
8861:
8857:
8854:
8852:
8849:
8847:
8844:
8842:
8839:
8837:
8834:
8833:
8831:
8827:
8821:
8818:
8816:
8813:
8811:
8810:Recursive set
8808:
8806:
8803:
8801:
8798:
8796:
8793:
8791:
8788:
8784:
8781:
8779:
8776:
8774:
8771:
8769:
8766:
8764:
8761:
8760:
8759:
8756:
8754:
8751:
8749:
8746:
8744:
8741:
8739:
8736:
8734:
8731:
8730:
8728:
8726:
8722:
8716:
8713:
8711:
8708:
8706:
8703:
8701:
8698:
8696:
8693:
8691:
8688:
8686:
8683:
8679:
8676:
8674:
8671:
8669:
8666:
8665:
8664:
8661:
8659:
8656:
8654:
8651:
8649:
8646:
8644:
8641:
8639:
8636:
8632:
8629:
8628:
8627:
8624:
8620:
8619:of arithmetic
8617:
8616:
8615:
8612:
8608:
8605:
8603:
8600:
8598:
8595:
8593:
8590:
8588:
8585:
8584:
8583:
8580:
8576:
8573:
8571:
8568:
8567:
8566:
8563:
8562:
8560:
8558:
8554:
8548:
8545:
8543:
8540:
8538:
8535:
8533:
8530:
8527:
8526:from ZFC
8523:
8520:
8518:
8515:
8509:
8506:
8505:
8504:
8501:
8499:
8496:
8494:
8491:
8490:
8489:
8486:
8484:
8481:
8479:
8476:
8474:
8471:
8469:
8466:
8464:
8461:
8459:
8456:
8455:
8453:
8451:
8447:
8437:
8436:
8432:
8431:
8426:
8425:non-Euclidean
8423:
8419:
8416:
8414:
8411:
8409:
8408:
8404:
8403:
8401:
8398:
8397:
8395:
8391:
8387:
8384:
8382:
8379:
8378:
8377:
8373:
8369:
8366:
8365:
8364:
8360:
8356:
8353:
8351:
8348:
8346:
8343:
8341:
8338:
8336:
8333:
8331:
8328:
8327:
8325:
8321:
8320:
8318:
8313:
8307:
8302:Example
8299:
8291:
8286:
8285:
8284:
8281:
8279:
8276:
8272:
8269:
8267:
8264:
8262:
8259:
8257:
8254:
8253:
8252:
8249:
8247:
8244:
8242:
8239:
8237:
8234:
8230:
8227:
8225:
8222:
8221:
8220:
8217:
8213:
8210:
8208:
8205:
8203:
8200:
8198:
8195:
8194:
8193:
8190:
8188:
8185:
8181:
8178:
8176:
8173:
8171:
8168:
8167:
8166:
8163:
8159:
8156:
8154:
8151:
8149:
8146:
8144:
8141:
8139:
8136:
8134:
8131:
8130:
8129:
8126:
8124:
8121:
8119:
8116:
8114:
8111:
8107:
8104:
8102:
8099:
8097:
8094:
8092:
8089:
8088:
8087:
8084:
8082:
8079:
8077:
8074:
8072:
8069:
8065:
8062:
8060:
8059:by definition
8057:
8056:
8055:
8052:
8048:
8045:
8044:
8043:
8040:
8038:
8035:
8033:
8030:
8028:
8025:
8023:
8020:
8019:
8016:
8013:
8011:
8007:
8002:
7996:
7992:
7982:
7979:
7977:
7974:
7972:
7969:
7967:
7964:
7962:
7959:
7957:
7954:
7952:
7949:
7947:
7946:Kripke–Platek
7944:
7942:
7939:
7935:
7932:
7930:
7927:
7926:
7925:
7922:
7921:
7919:
7915:
7907:
7904:
7903:
7902:
7899:
7897:
7894:
7890:
7887:
7886:
7885:
7882:
7880:
7877:
7875:
7872:
7870:
7867:
7865:
7862:
7859:
7855:
7851:
7848:
7844:
7841:
7839:
7836:
7834:
7831:
7830:
7829:
7825:
7822:
7821:
7819:
7817:
7813:
7809:
7801:
7798:
7796:
7793:
7791:
7790:constructible
7788:
7787:
7786:
7783:
7781:
7778:
7776:
7773:
7771:
7768:
7766:
7763:
7761:
7758:
7756:
7753:
7751:
7748:
7746:
7743:
7741:
7738:
7736:
7733:
7731:
7728:
7726:
7723:
7722:
7720:
7718:
7713:
7705:
7702:
7700:
7697:
7695:
7692:
7690:
7687:
7685:
7682:
7680:
7677:
7676:
7674:
7670:
7667:
7665:
7662:
7661:
7660:
7657:
7655:
7652:
7650:
7647:
7645:
7642:
7640:
7636:
7632:
7630:
7627:
7623:
7620:
7619:
7618:
7615:
7614:
7611:
7608:
7606:
7602:
7592:
7589:
7587:
7584:
7582:
7579:
7577:
7574:
7572:
7569:
7567:
7564:
7560:
7557:
7556:
7555:
7552:
7548:
7543:
7542:
7541:
7538:
7537:
7535:
7533:
7529:
7521:
7518:
7516:
7513:
7511:
7508:
7507:
7506:
7503:
7501:
7498:
7496:
7493:
7491:
7488:
7486:
7483:
7481:
7478:
7476:
7473:
7472:
7470:
7468:
7467:Propositional
7464:
7458:
7455:
7453:
7450:
7448:
7445:
7443:
7440:
7438:
7435:
7433:
7430:
7426:
7423:
7422:
7421:
7418:
7416:
7413:
7411:
7408:
7406:
7403:
7401:
7398:
7396:
7395:Logical truth
7393:
7391:
7388:
7387:
7385:
7383:
7379:
7376:
7374:
7370:
7364:
7361:
7359:
7356:
7354:
7351:
7349:
7346:
7344:
7341:
7339:
7335:
7331:
7327:
7325:
7322:
7320:
7317:
7315:
7311:
7308:
7307:
7305:
7303:
7297:
7292:
7286:
7283:
7281:
7278:
7276:
7273:
7271:
7268:
7266:
7263:
7261:
7258:
7256:
7253:
7251:
7248:
7246:
7243:
7241:
7238:
7236:
7233:
7231:
7228:
7224:
7221:
7220:
7219:
7216:
7215:
7213:
7209:
7205:
7198:
7193:
7191:
7186:
7184:
7179:
7178:
7175:
7163:
7155:
7154:
7151:
7137:
7134:
7132:
7129:
7125:
7122:
7121:
7120:
7117:
7115:
7112:
7110:
7107:
7105:
7102:
7100:
7096:
7093:
7091:
7088:
7086:
7085:
7081:
7079:
7076:
7074:
7073:
7069:
7067:
7064:
7063:
7060:
7054:
7053:
7049:
7047:
7044:
7042:
7039:
7037:
7034:
7030:
7027:
7026:
7025:
7024:
7020:
7019:
7017:
7015:
7011:
7008:
7006:
6999:
6987:
6984:
6983:
6982:
6978:
6975:
6973:
6970:
6968:
6965:
6961:
6957:
6954:
6952:
6951:
6947:
6945:
6942:
6941:
6940:
6937:
6936:
6933:
6927:
6924:
6922:
6921:
6917:
6915:
6912:
6910:
6907:
6905:
6902:
6898:
6897:
6893:
6889:
6886:
6885:
6884:
6883:
6879:
6878:
6877:
6874:
6872:
6869:
6868:
6866:
6864:
6863:
6858:
6855:
6853:
6849:
6839:
6836:
6834:
6831:
6829:
6826:
6824:
6821:
6819:
6816:
6814:
6811:
6809:
6805:
6804:Invented here
6802:
6800:
6797:
6795:
6792:
6790:
6787:
6785:
6782:
6780:
6777:
6775:
6772:
6770:
6767:
6766:
6764:
6762:
6758:
6752:
6749:
6747:
6746:
6742:
6741:
6739:
6737:
6733:
6727:
6723:
6720:
6718:
6715:
6714:
6712:
6708:
6702:
6699:
6697:
6694:
6692:
6689:
6687:
6684:
6680:
6677:
6676:
6675:
6672:
6668:
6667:
6663:
6661:
6660:
6656:
6655:
6653:
6649:
6646:
6645:
6644:
6641:
6640:
6638:
6636:
6632:
6626:
6623:
6621:
6618:
6616:
6613:
6611:
6608:
6606:
6603:
6601:
6598:
6596:
6593:
6592:
6590:
6588:
6584:
6578:
6575:
6573:
6570:
6568:
6567:False analogy
6565:
6563:
6560:
6558:
6554:
6551:
6547:
6544:
6542:
6539:
6538:
6537:
6536:Sampling bias
6534:
6532:
6529:
6528:
6526:
6524:
6520:
6514:
6511:
6509:
6506:
6505:
6503:
6501:
6500:
6499:Secundum quid
6495:
6489:
6486:
6484:
6481:
6479:
6476:
6475:
6473:
6471:
6467:
6461:
6458:
6456:
6453:
6449:
6446:
6445:
6444:
6443:False dilemma
6441:
6440:
6438:
6436:
6432:
6426:
6423:
6421:
6417:
6413:
6410:
6406:
6403:
6402:
6401:
6398:
6396:
6392:
6389:
6388:
6386:
6382:
6376:
6373:
6371:
6368:
6366:
6363:
6361:
6358:
6356:
6353:
6351:
6348:
6346:
6343:
6342:
6340:
6336:
6333:
6331:
6327:
6317:
6314:
6312:
6311:Illicit minor
6309:
6307:
6306:Illicit major
6304:
6302:
6299:
6297:
6294:
6292:
6289:
6287:
6284:
6282:
6279:
6277:
6274:
6273:
6271:
6269:
6265:
6259:
6256:
6254:
6251:
6249:
6246:
6244:
6241:
6240:
6238:
6236:
6231:
6225:
6222:
6220:
6217:
6215:
6212:
6210:
6207:
6205:
6202:
6200:
6197:
6196:
6194:
6192:
6187:
6184:
6182:
6178:
6173:
6169:
6161:
6156:
6154:
6149:
6147:
6142:
6141:
6138:
6132:
6128:
6125:
6124:"Quantifiers"
6121:
6117:
6113:
6110:
6106:
6105:
6103:
6100:
6097:
6091:
6087:
6083:
6079:
6075:
6074:
6069:
6065:
6064:
6060:
6055:
6054:0-521-83182-2
6051:
6047:
6043:
6040:
6036:
6033:
6029:
6026:
6023:
6019:
6015:
6011:
6010:Peirce, C. S.
6008:
6005:
6001:
5997:
5996:
5991:
5987:
5984:
5981:
5977:
5973:
5972:
5967:
5964:
5953:
5948:
5945:
5941:
5937:
5933:
5930:
5929:
5925:
5916:
5910:
5906:
5905:
5897:
5894:
5891:
5890:1-85506-029-9
5887:
5883:
5877:
5874:
5870:
5864:
5861:
5857:
5856:
5851:
5846:
5843:
5839:
5836:∈ {∀,∃}, cf.
5835:
5831:
5827:
5823:
5820:
5817:
5814:
5811:
5807:
5803:
5799:
5796:
5793:
5790:
5787:
5783:
5779:
5773:
5770:
5766:
5761:
5758:
5753:
5749:
5745:
5741:
5737:
5733:
5729:
5725:
5721:
5714:
5711:
5705:
5701:
5697:
5691:
5687:
5680:
5677:
5674:Here: p.p.344
5671:
5669:0-201-02988-X
5665:
5661:
5654:
5651:
5646:
5640:
5636:
5632:
5628:
5627:
5619:
5616:
5610:
5608:0-444-88074-7
5604:
5600:
5593:
5590:
5579:
5575:
5569:
5566:
5555:
5551:
5545:
5542:
5538:
5534:
5530:
5529:
5521:
5518:
5511:
5507:
5504:
5501:
5498:
5496:
5492:
5489:
5487:
5484:
5482:
5479:
5477:
5474:
5472:
5469:
5467:
5464:
5462:
5459:
5458:
5454:
5443:
5438:
5436:
5434:
5430:
5426:
5421:
5419:
5415:
5414:Alonzo Church
5411:
5407:
5403:
5399:
5398:
5393:
5389:
5385:
5381:
5377:
5373:
5369:
5365:
5361:
5357:
5353:
5349:
5344:
5342:
5338:
5334:
5330:
5326:
5322:
5318:
5314:
5310:
5306:
5294:
5290:
5286:
5281:
5279:
5275:
5271:
5267:
5263:
5259:
5255:
5254:
5249:
5248:Gottlob Frege
5245:
5243:
5239:
5235:
5231:
5224:
5220:
5216:
5214:
5210:
5205:
5203:
5199:
5195:
5191:
5187:
5180:
5175:
5172:
5169:
5166:
5163:
5159:
5156:
5155:
5154:
5151:
5134:
5128:
5125:
5122:
5119:
5116:
5110:
5104:
5101:
5096:
5092:
5088:
5080:
5077:
5067:
5066:
5065:
5063:
5059:
5055:
5051:
5029:
5026:
5023:
5020:
5017:
5011:
5007:
5003:
5000:
4995:
4991:
4981:
4978:
4971:
4963:
4962:
4961:
4959:
4951:
4949:
4947:
4928:
4925:
4914:
4908:
4905:
4900:
4897:
4894:
4890:
4886:
4883:
4880:
4875:
4871:
4864:
4861:
4858:
4852:
4846:
4843:
4836:
4835:
4834:
4832:
4826:
4822:
4815:
4791:
4787:
4783:
4778:
4775:
4772:
4768:
4764:
4761:
4758:
4753:
4749:
4742:
4737:
4733:
4707:
4706:
4705:
4703:
4684:
4681:
4670:
4664:
4661:
4656:
4653:
4650:
4646:
4642:
4639:
4636:
4631:
4627:
4620:
4617:
4614:
4608:
4598:
4597:
4596:
4594:
4588:
4584:
4577:
4553:
4549:
4545:
4540:
4537:
4534:
4530:
4526:
4523:
4520:
4515:
4511:
4504:
4499:
4495:
4466:
4465:
4464:
4461:
4457:
4450:
4447:of variables
4446:
4441:
4437:
4430:
4426:
4422:
4418:
4414:
4411:P defined on
4410:
4406:
4398:
4394:
4390:
4389:
4388:
4384:
4380:
4372:
4370:
4368:
4367:commutativity
4365:) to express
4364:
4360:
4356:
4352:
4348:
4344:
4340:
4336:
4332:
4328:
4324:
4320:
4316:
4312:
4308:
4304:
4300:
4296:
4292:
4288:
4284:
4280:
4276:
4272:
4269:
4265:
4261:
4257:
4253:
4234:
4224:
4221:
4218:
4207:
4204:
4199:
4196:
4193:
4189:
4185:
4182:
4179:
4174:
4170:
4163:
4160:
4154:
4151:
4146:
4143:
4140:
4136:
4132:
4129:
4126:
4121:
4117:
4110:
4100:
4097:
4094:
4084:
4065:
4061:
4057:
4054:
4051:
4046:
4042:
4035:
4030:
4026:
4015:
4014:
4013:
4011:
4007:
3983:
3979:
3975:
3972:
3969:
3964:
3960:
3953:
3948:
3944:
3940:
3930:
3929:
3928:
3926:
3921:
3916:
3914:
3908:
3904:
3897:
3893:
3889:
3885:
3881:
3875:
3871:
3864:
3860:
3856:
3850:
3846:
3839:
3835:
3831:
3827:
3803:
3799:
3795:
3792:
3789:
3784:
3780:
3773:
3768:
3764:
3753:
3752:
3751:
3749:
3743:
3739:
3732:
3728:
3724:
3720:
3716:
3710:
3706:
3699:
3695:
3691:
3687:
3683:
3679:
3673:
3669:
3662:
3658:
3654:
3648:
3644:
3637:
3633:
3629:
3625:
3601:
3597:
3593:
3590:
3587:
3582:
3578:
3571:
3566:
3562:
3551:
3550:
3549:
3547:
3543:
3539:
3535:
3530:
3526:
3519:
3515:
3511:
3504:
3497:
3493:
3490:. A formula
3489:
3485:
3481:
3458:
3455:
3452:
3446:
3443:
3434:
3431:
3428:
3422:
3419:
3410:
3398:
3394:
3392:
3388:
3384:
3380:
3376:
3372:
3368:
3364:
3360:
3356:
3334:
3331:
3328:
3322:
3319:
3310:
3307:
3304:
3298:
3295:
3286:
3276:
3275:
3274:
3272:
3268:
3264:
3259:
3255:
3251:
3243:
3241:
3239:
3231:
3227:
3223:
3219:
3215:
3211:
3207:
3206:
3205:
3200:
3196:
3192:
3188:
3184:
3183:
3182:
3180:
3176:
3168:
3164:
3161:
3157:
3156:
3155:
3149:
3145:
3141:
3137:
3136:
3135:
3133:
3128:
3114:
3111:
3108:
3100:
3096:
3085:
3069:
3066:
3063:
3055:
3051:
3039:
3037:
3033:
3029:
3024:
3020:
3012:
3008:this theory).
3007:
3003:
2985:
2982:
2978:
2957:
2949:
2945:
2943:
2939:
2934:
2920:
2900:
2880:
2860:
2849:
2845:
2841:
2837:
2830:
2821:
2819:
2817:
2813:
2809:
2804:
2802:
2798:
2779:
2773:
2767:
2760:
2756:
2752:
2746:
2737:
2731:
2727:
2723:
2719:
2703:
2702:
2701:
2699:
2695:
2676:
2670:
2664:
2657:
2653:
2649:
2643:
2634:
2628:
2624:
2620:
2616:
2600:
2599:
2598:
2581:
2572:
2566:
2563:
2560:
2555:
2551:
2544:
2534:
2533:
2532:
2515:
2509:
2503:
2499:
2495:
2491:
2481:
2480:
2479:
2462:
2453:
2447:
2441:
2437:
2433:
2426:
2416:
2415:
2414:
2412:
2393:
2387:
2381:
2377:
2373:
2369:
2359:
2358:
2357:
2355:
2351:
2347:
2343:
2339:
2331:
2329:
2327:
2322:
2320:
2316:
2311:
2308:
2304:
2300:
2296:
2292:
2288:
2284:
2280:
2276:
2254:
2251:
2240:
2237:
2234:
2228:
2225:
2219:
2213:
2200:
2197:
2189:
2172:
2169:
2157:
2154:
2147:
2144:
2141:
2134:
2131:
2128:
2117:
2100:
2097:
2086:
2083:
2080:
2074:
2071:
2065:
2059:
2046:
2043:
2035:
2018:
2015:
2008:
2005:
2002:
1990:
1987:
1980:
1977:
1974:
1963:
1962:
1961:
1959:
1955:
1954:
1949:
1945:
1941:
1937:
1932:
1930:
1926:
1918:
1914:
1910:
1906:
1902:
1901:
1900:
1894:
1890:
1886:
1882:
1878:
1877:
1876:
1872:
1864:
1859:
1856:
1855:
1854:
1852:
1848:
1840:
1836:
1833:
1829:
1828:
1827:
1825:
1822:Keywords for
1818:
1814:
1812:such that ...
1811:
1807:
1804:
1800:
1799:
1798:
1795:
1793:
1789:
1785:
1781:
1776:
1774:
1766:
1762:
1759:
1756:
1752:
1748:
1745:
1741:
1740:
1739:
1722:
1715:
1692:
1689:
1686:
1666:
1661:
1657:
1649:
1648:
1647:
1630:
1626:
1622:
1618:
1594:
1590:
1586:
1581:
1557:
1552:
1547:
1523:
1517:
1489:
1482:
1455:
1452:
1449:
1423:
1417:
1411:
1385:
1379:
1373:
1347:
1340:
1313:
1308:
1304:
1296:
1295:
1294:
1292:
1288:
1284:
1265:
1260:
1236:
1231:
1220:
1219:
1218:
1215:
1213:
1209:
1206:
1203:
1199:
1195:
1191:
1169:
1163:
1160:
1154:
1148:
1142:
1139:
1135:
1130:
1118:
1114:
1110:
1106:
1102:
1098:
1094:
1090:
1084:
1082:
1078:
1074:
1070:
1062:
1057:
1053:
1049:
1047:, and others;
1046:
1042:
1041:Alfred Tarski
1039:, devised by
1038:
1035:
1032:
1028:
1025:
1021:
1020:Alfred Tarski
1017:
1013:
1009:
1005:
1002:
1001:
1000:
998:
994:
990:
982:
977:
973:
970:
966:
965:
964:
962:
954:
953:
952:
950:
942:
938:
934:
930:
927:
923:
922:
921:
919:
915:
911:
906:
904:
900:
896:
892:
891:
881:
880:
879:
877:
869:
867:
865:
847:
843:
839:
836:
833:
828:
824:
820:
817:
795:
791:
787:
784:
780:
777:
774:
763:
762:binary digits
744:
741:
738:
732:
729:
704:
700:
693:
690:
687:
684:
681:
678:
670:
666:
659:
652:
633:
627:
623:
620:
617:
589:
585:
578:
575:
572:
569:
566:
563:
555:
551:
544:
537:
518:
512:
508:
505:
502:
474:
470:
466:
463:
460:
457:
452:
448:
441:
438:
426:
424:
422:
418:
413:
411:
407:
401:
399:
395:
391:
387:
371:
348:
342:
339:
325:
321:
317:
268:
264:
262:
258:
254:
235:
229:
226:
196:
180:
157:
151:
148:
137:
114:
110:
106:
102:
98:
87:
84:
76:
66:
63:and read the
62:
56:
53:
48:
39:
38:
33:
19:
9553:Type shifter
9523:Quantization
9473:Continuation
9340:Veridicality
9220:Exhaustivity
9185:Cumulativity
9133:
9104:Indexicality
9084:Definiteness
9079:Conditionals
9006:Logical form
8912:
8710:Ultraproduct
8557:Model theory
8522:Independence
8458:Formal proof
8450:Proof theory
8433:
8406:
8363:real numbers
8335:second-order
8246:Substitution
8191:
8123:Metalanguage
8064:conservative
8037:Axiom schema
7981:Constructive
7951:Morse–Kelley
7917:Set theories
7896:Aleph number
7889:inaccessible
7795:Grothendieck
7679:intersection
7580:
7566:Higher-order
7554:Second-order
7500:Truth tables
7457:Venn diagram
7240:Formal proof
7099:Naturalistic
7082:
7070:
7050:
7021:
7005:of relevance
6948:
6926:Whataboutism
6918:
6894:
6888:Godwin's law
6880:
6860:
6743:
6736:Consequences
6717:Law/Legality
6691:Single cause
6664:
6657:
6497:
6365:Loki's Wager
6345:Equivocation
6338:Equivocation
6234:
6090:the original
6071:
6068:"Quantifier"
6045:
6041:. Blackwell.
6038:
6031:
6021:
6017:
6013:
5999:
5993:
5979:
5969:
5955:. Retrieved
5939:
5932:Barwise, Jon
5926:Bibliography
5903:
5896:
5881:
5876:
5863:
5854:
5845:
5833:
5829:
5825:
5821:
5818:
5815:
5812:
5809:
5805:
5801:
5797:
5794:
5791:
5788:
5785:
5781:
5777:
5772:
5760:
5727:
5723:
5713:
5685:
5679:
5659:
5653:
5625:
5618:
5598:
5592:
5581:. Retrieved
5577:
5568:
5557:. Retrieved
5553:
5544:
5527:
5520:
5495:noun phrases
5422:
5395:
5391:
5387:
5383:
5379:
5375:
5371:
5367:
5363:
5359:
5355:
5345:
5329:completeness
5308:
5304:
5282:
5277:
5265:
5251:
5246:
5242:some-not-all
5241:
5237:
5228:
5212:
5206:
5197:
5193:
5189:
5184:
5152:
5149:
5057:
5053:
5049:
5047:
4958:section sign
4955:
4945:
4943:
4830:
4824:
4820:
4813:
4811:
4701:
4699:
4592:
4586:
4582:
4575:
4573:
4459:
4455:
4448:
4444:
4439:
4435:
4428:
4424:
4420:
4416:
4412:
4404:
4402:
4396:
4392:
4386:
4362:
4358:
4354:
4350:
4346:
4342:
4338:
4334:
4330:
4326:
4322:
4314:
4310:
4306:
4302:
4298:
4294:
4290:
4286:
4282:
4278:
4274:
4270:
4268:open formula
4263:
4259:
4255:
4249:
4009:
4005:
4003:
3924:
3917:
3912:
3906:
3902:
3895:
3891:
3887:
3883:
3879:
3873:
3869:
3862:
3858:
3854:
3848:
3844:
3837:
3833:
3829:
3825:
3823:
3747:
3741:
3737:
3730:
3726:
3722:
3718:
3714:
3708:
3704:
3697:
3693:
3689:
3685:
3681:
3677:
3671:
3667:
3660:
3656:
3652:
3646:
3642:
3635:
3631:
3627:
3623:
3621:
3545:
3541:
3537:
3533:
3528:
3524:
3517:
3513:
3502:
3495:
3491:
3487:
3477:
3390:
3386:
3382:
3378:
3374:
3370:
3366:
3362:
3358:
3354:
3352:
3266:
3247:
3237:
3235:
3229:
3225:
3221:
3217:
3213:
3209:
3203:
3198:
3194:
3190:
3186:
3172:
3166:
3162:
3153:
3147:
3146:is even and
3143:
3139:
3131:
3129:
3082:) is always
3040:
3035:
3031:
3022:
3016:
2935:
2844:model theory
2834:
2805:
2800:
2796:
2794:
2697:
2693:
2691:
2596:
2530:
2477:
2408:
2353:
2349:
2345:
2341:
2337:
2335:
2323:
2319:Example here
2312:
2306:
2302:
2298:
2294:
2290:
2286:
2282:
2278:
2274:
2272:
1957:
1952:
1947:
1933:
1928:
1924:
1922:
1916:
1912:
1908:
1904:
1898:
1892:
1888:
1884:
1880:
1874:
1846:
1844:
1838:
1831:
1821:
1816:
1809:
1802:
1796:
1791:
1787:
1783:
1779:
1777:
1772:
1770:
1750:
1737:
1645:
1290:
1286:
1282:
1280:
1216:
1211:
1207:
1201:
1197:
1193:
1189:
1116:
1112:
1108:
1104:
1096:
1092:
1088:
1085:
1066:
986:
975:
971:
960:
958:
946:
940:
936:
932:
928:
917:
907:
887:
885:
875:
873:
863:
810:abbreviates
430:
414:
402:
273:
109:open formula
100:
94:
79:
70:
59:Please help
54:
52:lead section
9468:Context set
9442:Type theory
9325:Subtrigging
9089:Disjunction
9016:Proposition
8820:Type theory
8768:undecidable
8700:Truth value
8587:equivalence
8266:non-logical
7879:Enumeration
7869:Isomorphism
7816:cardinality
7800:Von Neumann
7765:Ultrafilter
7730:Uncountable
7664:equivalence
7581:Quantifiers
7571:Fixed-point
7540:First-order
7420:Consistency
7405:Proposition
7382:Traditional
7353:Lindström's
7343:Compactness
7285:Type theory
7230:Cardinality
7119:Red herring
6876:Association
6557:Conjunction
6478:Composition
6375:Reification
6291:Existential
6243:Existential
5724:Cybernetics
5613:Here: p.497
5416:. In 1935,
4948:otherwise.
3915:otherwise.
3250:mathematics
3216:belongs to
3160:even number
3028:real number
1210:applies to
1200:applies to
1056:Paul Halmos
1045:Leon Henkin
949:disjunction
890:conjunction
136:first order
107:satisfy an
73:August 2022
9638:Categories
9618:Pragmatics
9265:Mirativity
9031:Speech act
8986:Entailment
8981:Denotation
8631:elementary
8324:arithmetic
8192:Quantifier
8170:functional
8042:Expression
7760:Transitive
7704:identities
7689:complement
7622:hereditary
7605:Set theory
7095:Moralistic
7029:Sealioning
7023:Ad nauseam
6950:Ipse dixit
6862:Ad hominem
6686:Regression
6488:Ecological
6301:Four terms
6219:Masked man
5765:Brown 2002
5695:3540058192
5583:2020-09-04
5559:2020-09-04
5512:References
5466:Almost all
5382:," and "(∃
5325:Kurt Gödel
5262:predicates
5186:Term logic
5162:almost all
5056:such that
4423:≤ 1. If
4383:measurable
4377:See also:
3684:for every
3208:For every
3002:equivalent
2913:such that
2873:such that
1960:is called
1887:such that
1869:See also:
261:subformula
101:quantifier
9664:Semantics
9417:Mereology
9353:Formalism
9235:Givenness
9160:Cataphora
9148:Phenomena
9139:Vagueness
9069:Ambiguity
9021:Reference
9001:Intension
8991:Extension
8902:Supertask
8805:Recursion
8763:decidable
8597:saturated
8575:of models
8498:deductive
8493:axiomatic
8413:Hilbert's
8400:Euclidean
8381:canonical
8304:axiomatic
8236:Signature
8165:Predicate
8054:Extension
7976:Ackermann
7901:Operation
7780:Universal
7770:Recursive
7745:Singleton
7740:Inhabited
7725:Countable
7715:Types of
7699:power set
7669:partition
7586:Predicate
7532:Predicate
7447:Syllogism
7437:Soundness
7410:Inference
7400:Tautology
7302:paradoxes
7136:Straw man
7014:Arguments
7003:fallacies
6977:Tradition
6967:Etymology
6939:Authority
6920:Tu quoque
6904:Bulverism
6674:Gambler's
6643:Animistic
6587:Ambiguity
6553:Base rate
6296:Necessity
6168:fallacies
6078:EMS Press
5869:summation
5752:121409759
5744:0011-4235
5704:1431-4657
5402:Whitehead
5207:In 1827,
5102:≤
5081:∈
5001:≤
4982:∈
4976:§
4926:≤
4898:−
4884:…
4853:
4829:which is
4776:−
4762:…
4716:∃
4682:≥
4654:−
4640:…
4609:
4591:which is
4538:−
4524:…
4475:∃
4215:⟹
4197:−
4183:…
4161:∧
4144:−
4130:…
4092:∀
4055:…
4023:∃
3973:…
3938:∃
3793:…
3761:∃
3591:…
3559:∀
3444:∨
3417:∃
3408:∀
3320:∨
3293:∃
3284:∀
3169:is prime.
3158:For some
3105:∅
3101:∈
3094:∃
3067:≠
3060:∅
3056:∈
3049:∀
2979:α
2958:α
2921:…
2881:…
2858:∃
2765:¬
2757:∈
2750:∀
2747:≡
2724:∈
2717:∃
2711:¬
2662:¬
2654:∈
2647:∃
2644:≡
2621:∈
2614:∀
2608:¬
2564:∧
2556:∈
2542:∃
2496:∈
2489:∃
2445:→
2438:∈
2424:∀
2374:∈
2367:∀
2255:ε
2226:−
2205:⇒
2201:δ
2173:∈
2167:∀
2158:∈
2152:∀
2142:δ
2139:∃
2129:ε
2126:∀
2101:ε
2072:−
2051:⇒
2047:δ
2019:∈
2013:∀
2003:δ
2000:∃
1991:∈
1985:∀
1975:ε
1972:∀
1944:pointwise
1845:Further,
1826:include:
1687:⋀
1658:⋀
1615:∃
1587:∈
1578:∃
1544:∃
1514:∃
1479:∃
1447:∃
1418:⋅
1409:∃
1371:∃
1337:∃
1305:⋁
1257:∀
1228:∃
1161:∨
1136:∈
1127:∀
1101:predicate
967:For some
924:For each
910:procedure
888:infinite
834:∧
778:∈
772:∀
691:∨
679:∨
621:∈
615:∃
576:∧
564:∧
506:∈
500:∀
398:Lindström
394:Mostowski
337:∃
334:¬
302:∃
282:∀
224:∃
204:∃
146:∀
122:∀
9571:See also
9456:Concepts
9330:Telicity
9165:Coercion
9119:Negation
9114:Modality
9064:Anaphora
8887:Logicism
8880:timeline
8856:Concrete
8715:Validity
8685:T-schema
8678:Kripke's
8673:Tarski's
8668:semantic
8658:Strength
8607:submodel
8602:spectrum
8570:function
8418:Tarski's
8407:Elements
8394:geometry
8350:Robinson
8271:variable
8256:function
8229:spectrum
8219:Sentence
8175:variable
8118:Language
8071:Relation
8032:Automata
8022:Alphabet
8006:language
7860:-jection
7838:codomain
7824:Function
7785:Universe
7755:Infinite
7659:Relation
7442:Validity
7432:Argument
7330:theorem,
7162:Category
6794:Ridicule
6779:Flattery
6769:Children
6666:Post hoc
6546:McNamara
6508:Accident
6483:Division
6330:Informal
6127:Archived
5978:, 1967.
5968:, 1879.
5938:, 2000.
5852:, 2004,
5439:See also
5276:'s 1903
4341:, like ∀
4305:>2 ∧
4273:>2 ∧
3173:In some
3150:is prime
2938:formulas
1063:Notation
995:include
324:negation
138:formula
9074:Binding
8829:Related
8626:Diagram
8524: (
8503:Hilbert
8488:Systems
8483:Theorem
8361:of the
8306:systems
8086:Formula
8081:Grammar
7997: (
7941:General
7654:Forcing
7639:Element
7559:Monadic
7334:paradox
7275:Theorem
7211:General
6981:Novelty
6956:Poverty
6818:Loyalty
6784:Novelty
6761:Emotion
6710:Appeals
6679:Inverse
6659:Cum hoc
6648:Furtive
6166:Common
6080:, 2001
5957:Aug 30,
5418:Gentzen
5406:Russell
5181:History
4266:of the
3901:, ...,
3868:, ...,
3843:, ...,
3736:, ...,
3725:, then
3703:, ...,
3666:, ...,
3641:, ...,
3523:, ...,
3510:Boolean
3501:, ...,
3220:, then
3004:to it (
1940:uniform
1851:pronoun
1817:x, ....
1782:" or "∃
905:words.
134:in the
9503:Monads
9050:Topics
8592:finite
8355:Skolem
8308:
8283:Theory
8251:Symbol
8241:String
8224:atomic
8101:ground
8096:closed
8091:atomic
8047:ground
8010:syntax
7906:binary
7833:domain
7750:Finite
7515:finite
7373:Logics
7332:
7280:Theory
7066:Cliché
7001:Other
6972:Nature
6960:Wealth
6595:Accent
6181:Formal
6052:
6018:et al.
5988:; and
5934:; and
5911:
5888:
5840:above.
5750:
5742:
5702:
5692:
5666:
5641:
5605:
5412:, and
5268:~, or
3692:. If
3254:syntax
3236:where
3154:means
3006:modulo
2948:theory
2846:, and
1421:
1415:
1383:
1377:
1099:) the
993:models
991:whose
935:· 2 =
903:finite
899:syntax
259:and a
9644:Logic
9195:De se
9099:Focus
9057:Areas
9026:Scope
8582:Model
8330:Peano
8187:Proof
8027:Arity
7956:Naive
7843:image
7775:Fuzzy
7735:Empty
7684:union
7629:Class
7270:Model
7260:Lemma
7218:Axiom
6828:Spite
6722:Stone
5748:S2CID
5410:Quine
5307:and ∃
5299:and Σ
4819:,...,
4581:,...,
4454:,...,
4434:,...,
3890:and
3532:) of
3263:scope
3224:·2 =
3212:, if
3193:·2 =
2315:scope
1950:from
1929:every
1834:, ...
1805:, ...
318:; in
316:duals
253:scope
97:logic
8705:Type
8508:list
8312:list
8289:list
8278:Term
8212:rank
8106:open
8000:list
7812:Maps
7717:sets
7576:Free
7546:list
7296:list
7223:list
6914:Tone
6789:Pity
6774:Fear
6172:list
6050:ISBN
5959:2018
5909:ISBN
5886:ISBN
5740:ISSN
5700:ISSN
5690:ISBN
5664:ISBN
5639:ISBN
5603:ISBN
5431:and
5404:and
5350:and
5240:and
5196:and
5194:Some
4944:and
4847:<
4700:and
4381:and
3911:) =
3882:) =
3853:) =
3746:) =
3717:) =
3680:) =
3651:) =
3482:for
3377:and
3357:and
3271:free
2344:and
2305:) =
2281:and
2252:<
2198:<
2145:>
2132:>
2098:<
2044:<
2006:>
1978:>
1942:and
1765:type
1751:type
1087:let
1050:The
1029:and
864:true
408:and
396:and
294:and
99:, a
9447:TTR
8392:of
8374:of
8322:of
7854:Sur
7828:Map
7635:Ur-
7617:Set
6233:In
6189:In
5732:doi
5631:doi
5533:doi
5400:of
5339:of
5331:of
5238:all
5190:All
5064:as
5052:in
4010:and
3828:of
3688:in
3626:of
3478:An
3381:in
3361:in
3269:is
3021:or
2806:In
2336:If
2328:".
1956:to
1214:".
1054:of
1027:ZFC
878:):
388:or
95:In
9640::
8778:NP
8402::
8396::
8326::
8003:),
7858:Bi
7850:In
7097:/
6979:/
6958:/
6806:/
6724:/
6555:/
6418:/
6414:/
6393:/
6104::
6076:,
6070:,
5746:.
5738:.
5726:.
5722:.
5698:.
5637:.
5576:.
5552:.
5531:,
5435:.
5408:,
5343:.
5319:,
5315:,
5280:.
5204:.
5198:No
5192:,
4827:-1
4589:-1
4419:≤
4369:.
3909:-1
3878:,
3876:-1
3851:-1
3744:-1
3713:,
3711:-1
3676:,
3674:-1
3649:-1
3389:,
3369:,
3228:+
3197:+
3189:,
3165:,
3142:,
2946:A
2842:,
2803:.
1915:=
1911:,
1891:=
1293::
1205:or
1196:,
1043:,
1018:,
1014:,
974:,
963::
951:,
939:+
931:,
920::
866:.
423:.
400:.
8954:e
8947:t
8940:v
8858:/
8773:P
8528:)
8314:)
8310:(
8207:∀
8202:!
8197:∃
8158:=
8153:↔
8148:→
8143:∧
8138:∨
8133:¬
7856:/
7852:/
7826:/
7637:)
7633:(
7520:∞
7510:3
7298:)
7196:e
7189:t
7182:v
6174:)
6170:(
6159:e
6152:t
6145:v
6098:.
6056:.
6006:.
5961:.
5917:.
5871:.
5834:Q
5830:y
5828:,
5826:x
5824:(
5822:p
5819:x
5816:Q
5813:y
5810:Q
5806:y
5804:,
5802:x
5800:(
5798:p
5795:y
5792:Q
5789:x
5786:Q
5782:Q
5778:Q
5767:.
5754:.
5734::
5728:5
5706:.
5672:.
5647:.
5633::
5611:.
5586:.
5562:.
5535::
5392:P
5388:P
5386:)
5384:x
5380:P
5376:P
5374:)
5372:x
5368:x
5364:x
5360:x
5356:x
5309:x
5305:x
5301:x
5297:x
5266:x
5135:.
5132:}
5129:2
5126:,
5123:1
5120:,
5117:0
5114:{
5111:=
5108:}
5105:4
5097:2
5093:n
5089::
5085:N
5078:n
5075:{
5058:n
5054:N
5050:n
5033:}
5030:2
5027:,
5024:1
5021:,
5018:0
5015:{
5012:=
5008:]
5004:4
4996:2
4992:n
4986:N
4979:n
4972:[
4946:T
4929:a
4923:}
4919:T
4915:=
4912:)
4909:w
4906:,
4901:1
4895:n
4891:v
4887:,
4881:,
4876:1
4872:v
4868:(
4865:F
4862::
4859:w
4856:{
4850:P
4844:0
4831:F
4825:n
4821:v
4817:1
4814:v
4797:)
4792:n
4788:x
4784:,
4779:1
4773:n
4769:x
4765:,
4759:,
4754:1
4750:x
4746:(
4743:A
4738:n
4734:x
4727:w
4724:e
4721:f
4702:F
4685:b
4679:}
4675:T
4671:=
4668:)
4665:w
4662:,
4657:1
4651:n
4647:v
4643:,
4637:,
4632:1
4628:v
4624:(
4621:F
4618::
4615:w
4612:{
4606:P
4593:T
4587:n
4583:v
4579:1
4576:v
4559:)
4554:n
4550:x
4546:,
4541:1
4535:n
4531:x
4527:,
4521:,
4516:1
4512:x
4508:(
4505:A
4500:n
4496:x
4489:y
4486:n
4483:a
4480:m
4460:n
4456:v
4452:1
4449:v
4445:F
4440:n
4436:x
4432:1
4429:x
4425:A
4421:b
4417:a
4413:X
4405:X
4397:n
4393:n
4363:x
4361:+
4359:y
4357:=
4355:y
4353:+
4351:x
4349:(
4347:y
4345:∀
4343:x
4335:x
4333:+
4331:y
4329:=
4327:y
4325:+
4323:x
4315:z
4313:=
4311:y
4309:+
4307:x
4303:n
4301:(
4299:z
4297:∃
4295:y
4293:∃
4291:x
4289:∃
4287:n
4283:z
4281:=
4279:y
4277:+
4275:x
4271:n
4260:x
4256:x
4235:.
4230:)
4225:z
4222:=
4219:y
4211:)
4208:z
4205:,
4200:1
4194:n
4190:x
4186:,
4180:,
4175:1
4171:x
4167:(
4164:A
4158:)
4155:y
4152:,
4147:1
4141:n
4137:x
4133:,
4127:,
4122:1
4118:x
4114:(
4111:A
4106:(
4101:z
4098:,
4095:y
4071:)
4066:n
4062:x
4058:,
4052:,
4047:1
4043:x
4039:(
4036:A
4031:n
4027:x
4006:n
3989:)
3984:n
3980:x
3976:,
3970:,
3965:1
3961:x
3957:(
3954:A
3949:n
3945:x
3941:!
3925:X
3913:F
3907:n
3903:v
3899:1
3896:v
3894:(
3892:H
3888:w
3884:T
3880:w
3874:n
3870:v
3866:1
3863:v
3861:(
3859:F
3855:T
3849:n
3845:v
3841:1
3838:v
3836:(
3834:H
3830:n
3826:H
3809:)
3804:n
3800:x
3796:,
3790:,
3785:1
3781:x
3777:(
3774:A
3769:n
3765:x
3748:F
3742:n
3738:v
3734:1
3731:v
3729:(
3727:G
3723:w
3719:F
3715:w
3709:n
3705:v
3701:1
3698:v
3696:(
3694:F
3690:X
3686:w
3682:T
3678:w
3672:n
3668:v
3664:1
3661:v
3659:(
3657:F
3653:T
3647:n
3643:v
3639:1
3636:v
3634:(
3632:G
3628:n
3624:G
3607:)
3602:n
3598:x
3594:,
3588:,
3583:1
3579:x
3575:(
3572:A
3567:n
3563:x
3546:F
3542:T
3538:X
3534:n
3529:n
3525:v
3521:1
3518:v
3516:(
3514:F
3506:n
3503:x
3499:1
3496:x
3492:A
3488:X
3462:)
3459:x
3456:,
3453:y
3450:(
3447:C
3441:)
3438:)
3435:y
3432:,
3429:x
3426:(
3423:B
3420:y
3414:(
3411:x
3391:x
3387:y
3385:(
3383:B
3379:y
3375:x
3371:x
3367:y
3365:(
3363:C
3359:y
3355:x
3338:)
3335:x
3332:,
3329:y
3326:(
3323:C
3317:)
3314:)
3311:y
3308:,
3305:x
3302:(
3299:B
3296:y
3290:(
3287:x
3267:x
3238:N
3232:,
3230:n
3226:n
3222:n
3218:N
3214:n
3210:n
3199:n
3195:n
3191:n
3187:n
3167:n
3163:n
3148:n
3144:n
3140:n
3115:x
3112:=
3109:x
3097:x
3070:x
3064:x
3052:x
3036:x
3032:n
2986:F
2983:Q
2901:x
2861:x
2831:.
2801:x
2797:x
2780:,
2777:)
2774:x
2771:(
2768:P
2761:D
2753:x
2744:)
2741:)
2738:x
2735:(
2732:P
2728:D
2720:x
2714:(
2698:x
2694:x
2677:,
2674:)
2671:x
2668:(
2665:P
2658:D
2650:x
2641:)
2638:)
2635:x
2632:(
2629:P
2625:D
2617:x
2611:(
2582:.
2579:)
2576:)
2573:x
2570:(
2567:P
2561:D
2552:x
2549:(
2545:x
2516:,
2513:)
2510:x
2507:(
2504:P
2500:D
2492:x
2463:.
2460:)
2457:)
2454:x
2451:(
2448:P
2442:D
2434:x
2431:(
2427:x
2394:.
2391:)
2388:x
2385:(
2382:P
2378:D
2370:x
2354:x
2350:x
2348:(
2346:P
2342:x
2338:D
2307:x
2303:x
2301:(
2299:f
2295:x
2291:ε
2287:δ
2283:x
2279:ε
2275:δ
2258:)
2248:|
2244:)
2241:h
2238:+
2235:x
2232:(
2229:f
2223:)
2220:x
2217:(
2214:f
2210:|
2194:|
2190:h
2186:|
2182:(
2177:R
2170:h
2162:R
2155:x
2148:0
2135:0
2104:)
2094:|
2090:)
2087:h
2084:+
2081:x
2078:(
2075:f
2069:)
2066:x
2063:(
2060:f
2056:|
2040:|
2036:h
2032:|
2028:(
2023:R
2016:h
2009:0
1995:R
1988:x
1981:0
1958:R
1953:R
1948:f
1925:s
1919:.
1917:n
1913:s
1909:n
1905:s
1895:.
1893:n
1889:s
1885:s
1881:n
1847:x
1839:x
1832:x
1810:x
1803:x
1792:x
1790:(
1788:P
1784:x
1780:x
1746:,
1723:P
1719:)
1716:x
1713:(
1693:P
1690:x
1667:P
1662:x
1631:P
1627:X
1623::
1619:x
1595:P
1591:X
1582:x
1558:P
1553:,
1548:x
1524:P
1518:x
1493:)
1490:P
1487:(
1483:x
1459:)
1456:P
1453::
1450:x
1444:(
1424:P
1412:x
1389:)
1386:P
1380:.
1374:x
1368:(
1348:P
1345:)
1341:x
1334:(
1314:P
1309:x
1291:x
1287:X
1283:P
1266:P
1261:x
1237:P
1232:x
1212:x
1208:Q
1202:x
1198:P
1194:X
1190:x
1176:)
1173:)
1170:x
1167:(
1164:Q
1158:)
1155:x
1152:(
1149:P
1146:(
1143:,
1140:X
1131:x
1117:x
1113:x
1111:(
1109:Q
1105:x
1103:"
1097:x
1095:(
1093:P
1089:X
1081:E
1077:∃
1073:A
1069:∀
1058:.
1033:;
976:n
972:n
943:.
941:n
937:n
933:n
929:n
848:2
844:1
840:=
837:1
829:2
825:0
821:=
818:0
796:2
792:x
788:=
785:x
781:B
775:x
748:}
745:1
742:,
739:0
736:{
733:=
730:B
710:)
705:n
701:a
697:(
694:P
688:.
685:.
682:.
676:)
671:1
667:a
663:(
660:P
637:)
634:x
631:(
628:P
624:D
618:x
595:)
590:n
586:a
582:(
579:P
573:.
570:.
567:.
561:)
556:1
552:a
548:(
545:P
522:)
519:x
516:(
513:P
509:D
503:x
480:}
475:n
471:a
467:.
464:.
461:.
458:,
453:1
449:a
445:{
442:=
439:D
372:P
352:)
349:x
346:(
343:P
340:x
239:)
236:x
233:(
230:P
227:x
181:P
161:)
158:x
155:(
152:P
149:x
86:)
80:(
75:)
71:(
67:.
57:.
34:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
