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A predicate is a statement or mathematical assertion that contains variables, sometimes referred to as predicate variables, and may be true or false depending on those variablesâ value or values.
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only includes predicates that apply to individual objects, other logics may allow predicates that apply to collections of objects defined by other predicates.
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249:. For instance, in a standard semantics for first-order logic, the formula
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is a symbol that represents a property or a relation. For instance, in the
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Problems in Set Theory, Mathematical Logic, and the Theory of
Algorithms
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is a predicate that applies to the individual constants
30:"Predicate (logic)" redirects here. For other uses, see
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Symbol representing a property or relation in logic
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341:{\displaystyle R}
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113:{\displaystyle a}
90:{\displaystyle P}
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2187:Recursive set
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1498:
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1436:by definition
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1323:KripkeâPlatek
1321:
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1309:
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1302:
1299:
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1199:
1198:
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1190:
1186:
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1167:constructible
1165:
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1128:
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875:
873:
870:
868:
865:
863:
860:
858:
855:
853:
850:
849:
847:
845:
844:Propositional
841:
835:
832:
830:
827:
825:
822:
820:
817:
815:
812:
810:
807:
803:
800:
799:
798:
795:
793:
790:
788:
785:
783:
780:
778:
775:
773:
772:Logical truth
770:
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747:
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738:
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733:
731:
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723:
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712:
708:
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688:
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669:
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648:
645:
643:
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623:
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582:
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568:
563:
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538:
529:
523:
519:
518:
513:
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487:
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457:
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452:
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435:
432:
428:
424:
421:
417:
413:
409:
405:
401:
397:
393:
390:
386:
382:
380:) predicates.
379:
375:
371:
367:
366:
365:
359:
357:
355:
351:
335:
315:
295:
287:
268:
265:
262:
256:
248:
244:
239:
237:
233:
229:
225:
221:
220:Gottlob Frege
218:According to
216:
202:
182:
162:
155:, the symbol
139:
136:
133:
127:
107:
100:
84:
77:, the symbol
61:
55:
48:
44:
40:
33:
19:
2289:
2087:Ultraproduct
1934:Model theory
1899:Independence
1835:Formal proof
1827:Proof theory
1810:
1783:
1740:real numbers
1712:second-order
1623:Substitution
1541:
1500:Metalanguage
1441:conservative
1414:Axiom schema
1358:Constructive
1328:MorseâKelley
1294:Set theories
1273:Aleph number
1266:inaccessible
1172:Grothendieck
1056:intersection
962:
943:Higher-order
931:Second-order
877:Truth tables
834:Venn diagram
617:Formal proof
516:
505:
430:
363:
240:
236:truth values
231:
227:
223:
217:
42:
36:
2333:Fuzzy logic
2197:Type theory
2145:undecidable
2077:Truth value
1964:equivalence
1643:non-logical
1256:Enumeration
1246:Isomorphism
1193:cardinality
1177:Von Neumann
1142:Ultrafilter
1107:Uncountable
1041:equivalence
958:Quantifiers
948:Fixed-point
917:First-order
797:Consistency
782:Proposition
759:Traditional
730:Lindström's
720:Compactness
662:Type theory
607:Cardinality
486:Truth value
481:Truthbearer
438:fuzzy logic
416:truth value
2312:Categories
2008:elementary
1701:arithmetic
1569:Quantifier
1547:functional
1419:Expression
1137:Transitive
1081:identities
1066:complement
999:hereditary
982:Set theory
527:0306477122
497:References
396:set theory
2279:Supertask
2182:Recursion
2140:decidable
1974:saturated
1952:of models
1875:deductive
1870:axiomatic
1790:Hilbert's
1777:Euclidean
1758:canonical
1681:axiomatic
1613:Signature
1542:Predicate
1431:Extension
1353:Ackermann
1278:Operation
1157:Universal
1147:Recursive
1122:Singleton
1117:Inhabited
1102:Countable
1092:Types of
1076:power set
1046:partition
963:Predicate
909:Predicate
824:Syllogism
814:Soundness
787:Inference
777:Tautology
679:paradoxes
412:functions
398:with the
247:relations
228:predicate
43:predicate
2264:Logicism
2257:timeline
2233:Concrete
2092:Validity
2062:T-schema
2055:Kripke's
2050:Tarski's
2045:semantic
2035:Strength
1984:submodel
1979:spectrum
1947:function
1795:Tarski's
1784:Elements
1771:geometry
1727:Robinson
1648:variable
1633:function
1606:spectrum
1596:Sentence
1552:variable
1495:Language
1448:Relation
1409:Automata
1399:Alphabet
1383:language
1237:-jection
1215:codomain
1201:Function
1162:Universe
1132:Infinite
1036:Relation
819:Validity
809:Argument
707:theorem,
514:(2003).
445:See also
2206:Related
2003:Diagram
1901: (
1880:Hilbert
1865:Systems
1860:Theorem
1738:of the
1683:systems
1463:Formula
1458:Grammar
1374: (
1318:General
1031:Forcing
1016:Element
936:Monadic
711:paradox
652:Theorem
588:General
431:unknown
410:(i.e.,
406:or set
241:In the
224:meaning
1969:finite
1732:Skolem
1685:
1660:Theory
1628:Symbol
1618:String
1601:atomic
1478:ground
1473:closed
1468:atomic
1424:ground
1387:syntax
1283:binary
1210:domain
1127:Finite
892:finite
750:Logics
709:
657:Theory
524:
232:domain
222:, the
1959:Model
1707:Peano
1564:Proof
1404:Arity
1333:Naive
1220:image
1152:Fuzzy
1112:Empty
1061:union
1006:Class
647:Model
637:Lemma
595:Axiom
389:terms
378:arity
226:of a
39:logic
2082:Type
1885:list
1689:list
1666:list
1655:Term
1589:rank
1483:open
1377:list
1189:Maps
1094:sets
953:Free
923:list
673:list
600:list
522:ISBN
308:and
195:and
41:, a
1769:of
1751:of
1699:of
1231:Sur
1205:Map
1012:Ur-
994:Set
436:In
425:In
418:).
394:In
383:In
368:In
215:.
37:In
2314::
2155:NP
1779::
1773::
1703::
1380:),
1235:Bi
1227:In
372:,
2235:/
2150:P
1905:)
1691:)
1687:(
1584:â
1579:!
1574:â
1535:=
1530:â
1525:â
1520:â§
1515:âš
1510:ÂŹ
1233:/
1229:/
1203:/
1014:)
1010:(
897:â
887:3
675:)
573:e
566:t
559:v
530:.
391:.
336:R
316:b
296:a
272:)
269:b
266:,
263:a
260:(
257:R
203:b
183:a
163:R
143:)
140:b
137:,
134:a
131:(
128:R
108:a
85:P
65:)
62:a
59:(
56:P
34:.
20:)
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