2158:
2228:
181:
of real numbers, the type of regular Cauchy sequences equipped with the usual notion of equivalence. Predicates and functions of real numbers need to be defined for regular Cauchy sequences and proven to be compatible with the equivalence relation. Typically (although it depends on the type theory
186:
will hold for functions between types (intensional functions), but not for functions between setoids (extensional functions). The term "set" is variously used either as a synonym of "type" or as a synonym of "setoid".
537:
2685:
1212:
1295:
436:
1609:
129:, normally only the truth of the proposition matters, not which proof was used. However, the CurryâHoward correspondence can turn proofs into
1767:
313:
555:
2374:
2194:
1622:
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93:). In contrast, setoids may be used when a difference between identity and equivalence must be maintained, often with an interpretation of
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1207:
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1627:
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551:
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1187:
133:, and differences between algorithms are often important. So proof theorists may prefer to identify a proposition with a
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1867:
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786:
212:
196:
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248:"The Interpretation of Intuitionistic Type Theory in Locally Cartesian Closed Categoriesâan Intuitionistic Perspective"
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1984:
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920:
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1979:
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1909:
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110:
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264:
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1031:
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731:
708:
291:
90:
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2667:
2581:
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2459:
2031:
1884:
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1394:
1130:
1036:
895:
880:
761:
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98:
2157:
126:
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2731:
2565:
2496:
2449:
2389:
2276:
2004:
1966:
1843:
1647:
1487:
1411:
1389:
1217:
1175:
1074:
1041:
905:
693:
604:
85:. Often in mathematics, when one defines an equivalence relation on a set, one immediately forms the
53:
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1989:
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122:
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641:
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309:
154:
149:
In type-theoretic foundations of mathematics, setoids may be used in a type theory that lacks
41:
125:(if any). A given proposition may have many proofs, of course; according to the principle of
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of proofs, considering proofs equivalent if they can be converted into one another through
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290:, Lecture Notes in Comput. Sci., vol. 902, Berlin: Springer, pp. 216â234,
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651:
130:
94:
402:
101:
equality (the equivalence relation, or the equality on the quotient set).
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16:"E-set" redirects here. For the technique in fertility medicine, see
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17:
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25:
Mathematical construction of a set with an equivalence relation
2172:
284:
Hofmann, Martin (1995), "A simple model for quotient types",
177:
in Martin-Löf's framework, therefore, one must work with a
331:
Barthe, Gilles; Capretta, Venanzio; Pons, Olivier (2003),
287:
Typed lambda calculi and applications (Edinburgh, 1995)
153:
to model general mathematical sets. For example, in
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109:In proof theory, particularly the proof theory of
252:Electronic Notes in Theoretical Computer Science
97:equality (the equality on the original set) and
2188:
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203:instead of an equivalence relation, called a
8:
2195:
2181:
2173:
1256:
851:
619:
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415:
295:
239:
207:setoid. One sometimes also considers a
215:or partial apartness (see e.g. Barthe
117:, one often identifies a mathematical
7:
199:, one often takes a setoid with an
74:Setoids are studied especially in
14:
340:Journal of Functional Programming
2226:
2156:
246:Alexandre Buisse, Peter Dybjer,
56:~. A setoid may also be called
1:
2117:History of mathematical logic
2042:Primitive recursive function
213:partial equivalence relation
115:CurryâHoward correspondence
2872:
2686:von NeumannâBernaysâGödel
1106:SchröderâBernstein theorem
833:Monadic predicate calculus
492:Foundations of mathematics
159:intuitionistic type theory
89:(turning equivalence into
83:foundations of mathematics
15:
2856:Equivalence (mathematics)
2487:One-to-one correspondence
2224:
2152:
2139:Philosophy of mathematics
2088:Automated theorem proving
1259:
1213:Von NeumannâBernaysâGödel
854:
382:Implementation of setoids
352:10.1017/S0956796802004501
333:"Setoids in type theory"
197:constructive mathematics
191:Constructive mathematics
167:regular Cauchy sequences
111:constructive mathematics
1789:Self-verifying theories
1610:Tarski's axiomatization
561:Tarski's undefinability
556:incompleteness theorems
2445:Constructible universe
2272:Constructibility (V=L)
2163:Mathematics portal
1774:Proof of impossibility
1422:propositional variable
732:Propositional calculus
161:, there is no type of
2668:Principia Mathematica
2502:Transfinite induction
2361:(i.e. set difference)
2032:Kolmogorov complexity
1985:Computably enumerable
1885:Model complete theory
1677:Principia Mathematica
737:Propositional formula
566:BanachâTarski paradox
265:"Bishop's set theory"
2742:Burali-Forti paradox
2497:Set-builder notation
2450:Continuum hypothesis
2390:Symmetric difference
1980:ChurchâTuring thesis
1967:Computability theory
1176:continuum hypothesis
694:Square of opposition
552:Gödel's completeness
54:equivalence relation
2703:TarskiâGrothendieck
2134:Mathematical object
2025:P versus NP problem
1990:Computable function
1784:Reverse mathematics
1710:Logical consequence
1587:primitive recursive
1582:elementary function
1355:Free/bound variable
1208:TarskiâGrothendieck
727:Logical connectives
657:Logical equivalence
507:Logical consequence
2292:Limitation of size
1932:Transfer principle
1895:Semantics of logic
1880:Categorical theory
1856:Non-standard model
1370:Logical connective
497:Information theory
446:Mathematical logic
306:10.1007/BFb0014055
201:apartness relation
2823:
2822:
2732:Russell's paradox
2681:ZermeloâFraenkel
2582:Dedekind-infinite
2455:Diagonal argument
2354:Cartesian product
2218:Set (mathematics)
2170:
2169:
2102:Abstract category
1905:Theories of truth
1715:Rule of inference
1705:Natural deduction
1686:
1685:
1231:
1230:
936:Cartesian product
841:
840:
747:Many-valued logic
722:Boolean functions
605:Russell's paradox
580:diagonal argument
477:First-order logic
315:978-3-540-59048-4
254:218 (2008) 21â32.
165:, only a type of
127:proof irrelevance
52:equipped with an
2863:
2836:Abstract algebra
2805:Bertrand Russell
2795:John von Neumann
2780:Abraham Fraenkel
2775:Richard Dedekind
2737:Suslin's problem
2648:Cantor's theorem
2365:De Morgan's laws
2230:
2197:
2190:
2183:
2174:
2161:
2160:
2112:History of logic
2107:Category of sets
2000:Decision problem
1779:Ordinal analysis
1720:Sequent calculus
1618:Boolean algebras
1558:
1557:
1532:
1503:logical/constant
1257:
1243:
1166:ZermeloâFraenkel
917:Set operations:
852:
789:
620:
600:LöwenheimâSkolem
487:Formal semantics
439:
432:
425:
416:
370:
337:
326:
299:
272:
271:
269:
261:
255:
244:
171:rational numbers
121:with its set of
2871:
2870:
2866:
2865:
2864:
2862:
2861:
2860:
2841:Category theory
2826:
2825:
2824:
2819:
2746:
2725:
2709:
2674:New Foundations
2621:
2511:
2430:Cardinal number
2413:
2399:
2340:
2231:
2222:
2206:
2201:
2171:
2166:
2155:
2148:
2093:Category theory
2083:Algebraic logic
2066:
2037:Lambda calculus
1975:Church encoding
1961:
1937:Truth predicate
1793:
1759:Complete theory
1682:
1551:
1547:
1543:
1538:
1530:
1250: and
1246:
1241:
1227:
1203:New Foundations
1171:axiom of choice
1154:
1116:Gödel numbering
1056: and
1048:
952:
837:
787:
768:
717:Boolean algebra
703:
667:Equiconsistency
632:Classical logic
609:
590:Halting problem
578: and
554: and
542: and
541:
536:Theorems (
531:
448:
443:
378:
335:
330:
316:
283:
280:
275:
267:
263:
262:
258:
245:
241:
237:
225:
211:setoid using a
193:
184:axiom of choice
147:
139:beta conversion
107:
69:extensional set
26:
21:
12:
11:
5:
2869:
2867:
2859:
2858:
2853:
2848:
2843:
2838:
2828:
2827:
2821:
2820:
2818:
2817:
2812:
2810:Thoralf Skolem
2807:
2802:
2797:
2792:
2787:
2782:
2777:
2772:
2767:
2762:
2756:
2754:
2748:
2747:
2745:
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2739:
2734:
2728:
2726:
2724:
2723:
2720:
2714:
2711:
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2708:
2707:
2706:
2705:
2700:
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2694:
2693:
2678:
2677:
2676:
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2663:
2662:
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2650:
2645:
2640:
2635:
2629:
2627:
2623:
2622:
2620:
2619:
2614:
2609:
2604:
2595:
2590:
2585:
2575:
2570:
2569:
2568:
2563:
2558:
2548:
2538:
2533:
2528:
2522:
2520:
2513:
2512:
2510:
2509:
2504:
2499:
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2492:Ordinal number
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2484:
2479:
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2447:
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2437:
2427:
2422:
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2414:
2412:
2411:
2408:
2404:
2401:
2400:
2398:
2397:
2392:
2387:
2382:
2377:
2372:
2370:Disjoint union
2367:
2362:
2356:
2350:
2348:
2342:
2341:
2339:
2338:
2337:
2336:
2331:
2320:
2319:
2317:Martin's axiom
2314:
2309:
2304:
2299:
2294:
2289:
2284:
2282:Extensionality
2279:
2274:
2269:
2268:
2267:
2262:
2257:
2247:
2241:
2239:
2233:
2232:
2225:
2223:
2221:
2220:
2214:
2212:
2208:
2207:
2202:
2200:
2199:
2192:
2185:
2177:
2168:
2167:
2153:
2150:
2149:
2147:
2146:
2141:
2136:
2131:
2126:
2125:
2124:
2114:
2109:
2104:
2095:
2090:
2085:
2080:
2078:Abstract logic
2074:
2072:
2068:
2067:
2065:
2064:
2059:
2057:Turing machine
2054:
2049:
2044:
2039:
2034:
2029:
2028:
2027:
2022:
2017:
2012:
2007:
1997:
1995:Computable set
1992:
1987:
1982:
1977:
1971:
1969:
1963:
1962:
1960:
1959:
1954:
1949:
1944:
1939:
1934:
1929:
1924:
1923:
1922:
1917:
1912:
1902:
1897:
1892:
1890:Satisfiability
1887:
1882:
1877:
1876:
1875:
1865:
1864:
1863:
1853:
1852:
1851:
1846:
1841:
1836:
1831:
1821:
1820:
1819:
1814:
1807:Interpretation
1803:
1801:
1795:
1794:
1792:
1791:
1786:
1781:
1776:
1771:
1761:
1756:
1755:
1754:
1753:
1752:
1742:
1737:
1727:
1722:
1717:
1712:
1707:
1702:
1696:
1694:
1688:
1687:
1684:
1683:
1681:
1680:
1672:
1671:
1670:
1669:
1664:
1663:
1662:
1657:
1652:
1632:
1631:
1630:
1628:minimal axioms
1625:
1614:
1613:
1612:
1601:
1600:
1599:
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1589:
1584:
1579:
1574:
1561:
1559:
1540:
1539:
1537:
1536:
1535:
1534:
1522:
1517:
1516:
1515:
1510:
1505:
1500:
1490:
1485:
1480:
1475:
1474:
1473:
1468:
1458:
1457:
1456:
1451:
1446:
1441:
1431:
1426:
1425:
1424:
1419:
1414:
1404:
1403:
1402:
1397:
1392:
1387:
1382:
1377:
1367:
1362:
1357:
1352:
1351:
1350:
1345:
1340:
1335:
1325:
1320:
1318:Formation rule
1315:
1310:
1309:
1308:
1303:
1293:
1292:
1291:
1281:
1276:
1271:
1266:
1260:
1254:
1237:Formal systems
1233:
1232:
1229:
1228:
1226:
1225:
1220:
1215:
1210:
1205:
1200:
1195:
1190:
1185:
1180:
1179:
1178:
1173:
1162:
1160:
1156:
1155:
1153:
1152:
1151:
1150:
1140:
1135:
1134:
1133:
1126:Large cardinal
1123:
1118:
1113:
1108:
1103:
1089:
1088:
1087:
1082:
1077:
1062:
1060:
1050:
1049:
1047:
1046:
1045:
1044:
1039:
1034:
1024:
1019:
1014:
1009:
1004:
999:
994:
989:
984:
979:
974:
969:
963:
961:
954:
953:
951:
950:
949:
948:
943:
938:
933:
928:
923:
915:
914:
913:
908:
898:
893:
891:Extensionality
888:
886:Ordinal number
883:
873:
868:
867:
866:
855:
849:
843:
842:
839:
838:
836:
835:
830:
825:
820:
815:
810:
805:
804:
803:
793:
792:
791:
778:
776:
770:
769:
767:
766:
765:
764:
759:
754:
744:
739:
734:
729:
724:
719:
713:
711:
705:
704:
702:
701:
696:
691:
686:
681:
676:
671:
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639:
634:
628:
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611:
610:
608:
607:
602:
597:
592:
587:
582:
570:Cantor's
568:
563:
558:
548:
546:
533:
532:
530:
529:
524:
519:
514:
509:
504:
499:
494:
489:
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469:
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467:
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419:
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377:
376:External links
374:
373:
372:
346:(2): 261â293,
328:
314:
297:10.1.1.55.4629
279:
276:
274:
273:
256:
238:
236:
233:
232:
231:
224:
221:
219:, section 1).
192:
189:
155:Per Martin-Löf
151:quotient types
146:
143:
106:
103:
80:type-theoretic
24:
13:
10:
9:
6:
4:
3:
2:
2868:
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2852:
2849:
2847:
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2839:
2837:
2834:
2833:
2831:
2816:
2815:Ernst Zermelo
2813:
2811:
2808:
2806:
2803:
2801:
2800:Willard Quine
2798:
2796:
2793:
2791:
2788:
2786:
2783:
2781:
2778:
2776:
2773:
2771:
2768:
2766:
2763:
2761:
2758:
2757:
2755:
2753:
2752:Set theorists
2749:
2743:
2740:
2738:
2735:
2733:
2730:
2729:
2727:
2721:
2719:
2716:
2715:
2712:
2704:
2701:
2699:
2698:KripkeâPlatek
2696:
2692:
2689:
2688:
2687:
2684:
2683:
2682:
2679:
2675:
2672:
2671:
2670:
2669:
2665:
2661:
2658:
2657:
2656:
2653:
2652:
2649:
2646:
2644:
2641:
2639:
2636:
2634:
2631:
2630:
2628:
2624:
2618:
2615:
2613:
2610:
2608:
2605:
2603:
2601:
2596:
2594:
2591:
2589:
2586:
2583:
2579:
2576:
2574:
2571:
2567:
2564:
2562:
2559:
2557:
2554:
2553:
2552:
2549:
2546:
2542:
2539:
2537:
2534:
2532:
2529:
2527:
2524:
2523:
2521:
2518:
2514:
2508:
2505:
2503:
2500:
2498:
2495:
2493:
2490:
2488:
2485:
2483:
2480:
2478:
2475:
2471:
2468:
2466:
2463:
2462:
2461:
2458:
2456:
2453:
2451:
2448:
2446:
2443:
2441:
2438:
2435:
2431:
2428:
2426:
2423:
2421:
2418:
2417:
2415:
2409:
2406:
2405:
2402:
2396:
2393:
2391:
2388:
2386:
2383:
2381:
2378:
2376:
2373:
2371:
2368:
2366:
2363:
2360:
2357:
2355:
2352:
2351:
2349:
2347:
2343:
2335:
2334:specification
2332:
2330:
2327:
2326:
2325:
2322:
2321:
2318:
2315:
2313:
2310:
2308:
2305:
2303:
2300:
2298:
2295:
2293:
2290:
2288:
2285:
2283:
2280:
2278:
2275:
2273:
2270:
2266:
2263:
2261:
2258:
2256:
2253:
2252:
2251:
2248:
2246:
2243:
2242:
2240:
2238:
2234:
2229:
2219:
2216:
2215:
2213:
2209:
2205:
2198:
2193:
2191:
2186:
2184:
2179:
2178:
2175:
2165:
2164:
2159:
2151:
2145:
2142:
2140:
2137:
2135:
2132:
2130:
2127:
2123:
2120:
2119:
2118:
2115:
2113:
2110:
2108:
2105:
2103:
2099:
2096:
2094:
2091:
2089:
2086:
2084:
2081:
2079:
2076:
2075:
2073:
2069:
2063:
2060:
2058:
2055:
2053:
2052:Recursive set
2050:
2048:
2045:
2043:
2040:
2038:
2035:
2033:
2030:
2026:
2023:
2021:
2018:
2016:
2013:
2011:
2008:
2006:
2003:
2002:
2001:
1998:
1996:
1993:
1991:
1988:
1986:
1983:
1981:
1978:
1976:
1973:
1972:
1970:
1968:
1964:
1958:
1955:
1953:
1950:
1948:
1945:
1943:
1940:
1938:
1935:
1933:
1930:
1928:
1925:
1921:
1918:
1916:
1913:
1911:
1908:
1907:
1906:
1903:
1901:
1898:
1896:
1893:
1891:
1888:
1886:
1883:
1881:
1878:
1874:
1871:
1870:
1869:
1866:
1862:
1861:of arithmetic
1859:
1858:
1857:
1854:
1850:
1847:
1845:
1842:
1840:
1837:
1835:
1832:
1830:
1827:
1826:
1825:
1822:
1818:
1815:
1813:
1810:
1809:
1808:
1805:
1804:
1802:
1800:
1796:
1790:
1787:
1785:
1782:
1780:
1777:
1775:
1772:
1769:
1768:from ZFC
1765:
1762:
1760:
1757:
1751:
1748:
1747:
1746:
1743:
1741:
1738:
1736:
1733:
1732:
1731:
1728:
1726:
1723:
1721:
1718:
1716:
1713:
1711:
1708:
1706:
1703:
1701:
1698:
1697:
1695:
1693:
1689:
1679:
1678:
1674:
1673:
1668:
1667:non-Euclidean
1665:
1661:
1658:
1656:
1653:
1651:
1650:
1646:
1645:
1643:
1640:
1639:
1637:
1633:
1629:
1626:
1624:
1621:
1620:
1619:
1615:
1611:
1608:
1607:
1606:
1602:
1598:
1595:
1593:
1590:
1588:
1585:
1583:
1580:
1578:
1575:
1573:
1570:
1569:
1567:
1563:
1562:
1560:
1555:
1549:
1544:Example
1541:
1533:
1528:
1527:
1526:
1523:
1521:
1518:
1514:
1511:
1509:
1506:
1504:
1501:
1499:
1496:
1495:
1494:
1491:
1489:
1486:
1484:
1481:
1479:
1476:
1472:
1469:
1467:
1464:
1463:
1462:
1459:
1455:
1452:
1450:
1447:
1445:
1442:
1440:
1437:
1436:
1435:
1432:
1430:
1427:
1423:
1420:
1418:
1415:
1413:
1410:
1409:
1408:
1405:
1401:
1398:
1396:
1393:
1391:
1388:
1386:
1383:
1381:
1378:
1376:
1373:
1372:
1371:
1368:
1366:
1363:
1361:
1358:
1356:
1353:
1349:
1346:
1344:
1341:
1339:
1336:
1334:
1331:
1330:
1329:
1326:
1324:
1321:
1319:
1316:
1314:
1311:
1307:
1304:
1302:
1301:by definition
1299:
1298:
1297:
1294:
1290:
1287:
1286:
1285:
1282:
1280:
1277:
1275:
1272:
1270:
1267:
1265:
1262:
1261:
1258:
1255:
1253:
1249:
1244:
1238:
1234:
1224:
1221:
1219:
1216:
1214:
1211:
1209:
1206:
1204:
1201:
1199:
1196:
1194:
1191:
1189:
1188:KripkeâPlatek
1186:
1184:
1181:
1177:
1174:
1172:
1169:
1168:
1167:
1164:
1163:
1161:
1157:
1149:
1146:
1145:
1144:
1141:
1139:
1136:
1132:
1129:
1128:
1127:
1124:
1122:
1119:
1117:
1114:
1112:
1109:
1107:
1104:
1101:
1097:
1093:
1090:
1086:
1083:
1081:
1078:
1076:
1073:
1072:
1071:
1067:
1064:
1063:
1061:
1059:
1055:
1051:
1043:
1040:
1038:
1035:
1033:
1032:constructible
1030:
1029:
1028:
1025:
1023:
1020:
1018:
1015:
1013:
1010:
1008:
1005:
1003:
1000:
998:
995:
993:
990:
988:
985:
983:
980:
978:
975:
973:
970:
968:
965:
964:
962:
960:
955:
947:
944:
942:
939:
937:
934:
932:
929:
927:
924:
922:
919:
918:
916:
912:
909:
907:
904:
903:
902:
899:
897:
894:
892:
889:
887:
884:
882:
878:
874:
872:
869:
865:
862:
861:
860:
857:
856:
853:
850:
848:
844:
834:
831:
829:
826:
824:
821:
819:
816:
814:
811:
809:
806:
802:
799:
798:
797:
794:
790:
785:
784:
783:
780:
779:
777:
775:
771:
763:
760:
758:
755:
753:
750:
749:
748:
745:
743:
740:
738:
735:
733:
730:
728:
725:
723:
720:
718:
715:
714:
712:
710:
709:Propositional
706:
700:
697:
695:
692:
690:
687:
685:
682:
680:
677:
675:
672:
668:
665:
664:
663:
660:
658:
655:
653:
650:
648:
645:
643:
640:
638:
637:Logical truth
635:
633:
630:
629:
627:
625:
621:
618:
616:
612:
606:
603:
601:
598:
596:
593:
591:
588:
586:
583:
581:
577:
573:
569:
567:
564:
562:
559:
557:
553:
550:
549:
547:
545:
539:
534:
528:
525:
523:
520:
518:
515:
513:
510:
508:
505:
503:
500:
498:
495:
493:
490:
488:
485:
483:
480:
478:
475:
473:
470:
466:
463:
462:
461:
458:
457:
455:
451:
447:
440:
435:
433:
428:
426:
421:
420:
417:
411:
409:
404:
401:
399:
397:
392:
389:
387:
383:
380:
379:
375:
369:
365:
361:
357:
353:
349:
345:
341:
334:
329:
325:
321:
317:
311:
307:
303:
298:
293:
289:
288:
282:
281:
277:
266:
260:
257:
253:
249:
243:
240:
234:
230:
227:
226:
222:
220:
218:
214:
210:
206:
202:
198:
190:
188:
185:
180:
176:
175:real analysis
172:
168:
164:
160:
156:
152:
144:
142:
141:or the like.
140:
136:
132:
128:
124:
120:
116:
113:based on the
112:
104:
102:
100:
96:
92:
88:
84:
81:
77:
72:
70:
66:
64:
59:
55:
51:
47:
43:
39:
35:
31:
23:
19:
2846:Proof theory
2765:Georg Cantor
2760:Paul Bernays
2691:MorseâKelley
2666:
2599:
2598:Subset
2545:hereditarily
2507:Venn diagram
2465:ordered pair
2380:Intersection
2324:Axiom schema
2154:
1952:Ultraproduct
1799:Model theory
1764:Independence
1700:Formal proof
1692:Proof theory
1675:
1648:
1605:real numbers
1577:second-order
1488:Substitution
1365:Metalanguage
1306:conservative
1279:Axiom schema
1223:Constructive
1193:MorseâKelley
1159:Set theories
1138:Aleph number
1131:inaccessible
1037:Grothendieck
921:intersection
808:Higher-order
796:Second-order
742:Truth tables
699:Venn diagram
482:Formal proof
407:
395:
343:
339:
286:
270:. p. 9.
259:
251:
242:
216:
208:
205:constructive
204:
194:
178:
163:real numbers
148:
134:
108:
105:Proof theory
87:quotient set
76:proof theory
73:
68:
61:
57:
49:
37:
33:
27:
22:
2851:Type theory
2790:Thomas Jech
2633:Alternative
2612:Uncountable
2566:Ultrafilter
2425:Cardinality
2329:replacement
2277:Determinacy
2062:Type theory
2010:undecidable
1942:Truth value
1829:equivalence
1508:non-logical
1121:Enumeration
1111:Isomorphism
1058:cardinality
1042:Von Neumann
1007:Ultrafilter
972:Uncountable
906:equivalence
823:Quantifiers
813:Fixed-point
782:First-order
662:Consistency
647:Proposition
624:Traditional
595:Lindström's
585:Compactness
527:Type theory
472:Cardinality
182:used), the
145:Type theory
119:proposition
99:extensional
95:intensional
30:mathematics
2830:Categories
2785:Kurt Gödel
2770:Paul Cohen
2607:Transitive
2375:Identities
2359:Complement
2346:Operations
2307:Regularity
2245:Adjunction
2204:Set theory
1873:elementary
1566:arithmetic
1434:Quantifier
1412:functional
1284:Expression
1002:Transitive
946:identities
931:complement
864:hereditary
847:Set theory
403:Bishop set
278:References
131:algorithms
40:, ~) is a
2718:Paradoxes
2638:Axiomatic
2617:Universal
2593:Singleton
2588:Recursive
2531:Countable
2526:Amorphous
2385:Power set
2302:Power set
2260:dependent
2255:countable
2144:Supertask
2047:Recursion
2005:decidable
1839:saturated
1817:of models
1740:deductive
1735:axiomatic
1655:Hilbert's
1642:Euclidean
1623:canonical
1546:axiomatic
1478:Signature
1407:Predicate
1296:Extension
1218:Ackermann
1143:Operation
1022:Universal
1012:Recursive
987:Singleton
982:Inhabited
967:Countable
957:Types of
941:power set
911:partition
828:Predicate
774:Predicate
689:Syllogism
679:Soundness
652:Inference
642:Tautology
544:paradoxes
292:CiteSeerX
2722:Problems
2626:Theories
2602:Superset
2578:Infinite
2407:Concepts
2287:Infinity
2211:Overview
2129:Logicism
2122:timeline
2098:Concrete
1957:Validity
1927:T-schema
1920:Kripke's
1915:Tarski's
1910:semantic
1900:Strength
1849:submodel
1844:spectrum
1812:function
1660:Tarski's
1649:Elements
1636:geometry
1592:Robinson
1513:variable
1498:function
1471:spectrum
1461:Sentence
1417:variable
1360:Language
1313:Relation
1274:Automata
1264:Alphabet
1248:language
1102:-jection
1080:codomain
1066:Function
1027:Universe
997:Infinite
901:Relation
684:Validity
674:Argument
572:theorem,
368:10069160
229:Groupoid
223:See also
173:. To do
91:equality
2660:General
2655:Zermelo
2561:subbase
2543: (
2482:Forcing
2460:Element
2432: (
2410:Methods
2297:Pairing
2071:Related
1868:Diagram
1766: (
1745:Hilbert
1730:Systems
1725:Theorem
1603:of the
1548:systems
1328:Formula
1323:Grammar
1239: (
1183:General
896:Forcing
881:Element
801:Monadic
576:paradox
517:Theorem
453:General
405:at the
393:at the
360:1985376
324:1477985
209:partial
78:and in
2551:Filter
2541:Finite
2477:Family
2420:Almost
2265:global
2250:Choice
2237:Axioms
1834:finite
1597:Skolem
1550:
1525:Theory
1493:Symbol
1483:String
1466:atomic
1343:ground
1338:closed
1333:atomic
1289:ground
1252:syntax
1148:binary
1075:domain
992:Finite
757:finite
615:Logics
574:
522:Theory
391:Setoid
366:
358:
322:
312:
294:
217:et al.
179:setoid
135:setoid
123:proofs
63:Bishop
34:setoid
2643:Naive
2573:Fuzzy
2536:Empty
2519:types
2470:tuple
2440:Class
2434:large
2395:Union
2312:Union
1824:Model
1572:Peano
1429:Proof
1269:Arity
1198:Naive
1085:image
1017:Fuzzy
977:Empty
926:union
871:Class
512:Model
502:Lemma
460:Axiom
364:S2CID
336:(PDF)
268:(PDF)
235:Notes
67:, or
58:E-set
18:e-SET
2556:base
1947:Type
1750:list
1554:list
1531:list
1520:Term
1454:rank
1348:open
1242:list
1054:Maps
959:sets
818:Free
788:list
538:list
465:list
310:ISBN
46:type
44:(or
32:, a
2517:Set
1634:of
1616:of
1564:of
1096:Sur
1070:Map
877:Ur-
859:Set
410:Lab
398:Lab
386:Coq
384:in
348:doi
302:doi
195:In
169:of
157:'s
65:set
42:set
28:In
2832::
2020:NP
1644::
1638::
1568::
1245:),
1100:Bi
1092:In
362:,
356:MR
354:,
344:13
342:,
338:,
320:MR
318:,
308:,
300:,
250:,
71:.
60:,
48:)
2600:·
2584:)
2580:(
2547:)
2436:)
2196:e
2189:t
2182:v
2100:/
2015:P
1770:)
1556:)
1552:(
1449:â
1444:!
1439:â
1400:=
1395:â
1390:â
1385:â§
1380:âš
1375:ÂŹ
1098:/
1094:/
1068:/
879:)
875:(
762:â
752:3
540:)
438:e
431:t
424:v
408:n
396:n
371:.
350::
327:.
304::
50:X
38:X
36:(
20:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.