59:
The divisions between these areas, along with the divisions between mathematical logic and the rest of mathematics, are not completely sharp, with many areas of research and methods overlapping and reinforcing each other.
29:
Mathematical logic is the study of formal logic within mathematics. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power.
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On
Formally Undecidable Propositions of Principia Mathematica and Related Systems
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72:
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This category has the following 34 subcategories, out of 34 total.
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359:
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838:
The following 199 pages are in this category, out of 199 total.
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1644:
Proof sketch for Gödel's first incompleteness theorem
1381:
1281:
Original proof of Gödel's completeness theorem
2008:
1713:Reverse Mathematics: Proofs from the Inside Out
545:Large-scale mathematical formalization projects
65:
33:Mathematical logic is divided into four parts:
1177:Extension by new constant and function names
1355:Implementation of mathematics in set theory
966:Theories of iterated inductive definitions
778:Theorems in the foundations of mathematics
1825:Structuralism (philosophy of mathematics)
1785:Simplification of disjunctive antecedents
1728:Robinson's joint consistency theorem
914:Algebraic semantics (mathematical logic)
840:This list may not reflect recent changes
2009:
1323:HilbertâBernays provability conditions
835:Pages in category "Mathematical logic"
1805:List of statements independent of ZFC
1882:Tarski's undefinability theorem
1291:Gödel's incompleteness theorems
167:
50:, also known as computability theory
13:
1580:Notre Dame Journal of Formal Logic
1476:List of axiomatic systems in logic
844:
174:
166:
14:
2038:
1409:König's theorem (set theory)
1365:Independence (mathematical logic)
1266:Glossary of Principia Mathematica
867:List of mathematical logic topics
1860:Glossary of mathematical symbols
1570:Non-standard model of arithmetic
971:BĂŒchi-Elgot-Trakhtenbrot theorem
666:Mathematical logic organizations
1182:Extensions of First Order Logic
1907:Timeline of mathematical logic
1830:Structure (mathematical logic)
1624:Predicate (mathematical logic)
1404:Knuth's Simpath algorithm
934:Archive for Mathematical Logic
505:Mathematical logic hierarchies
1:
1815:Strength (mathematical logic)
1249:Friedman's SSCG function
961:Boolean differential calculus
481:Formal theories of arithmetic
1810:Stratification (mathematics)
1461:Literal (mathematical logic)
1204:List of first-order theories
1100:Diagram (mathematical logic)
833:
414:Constructivism (mathematics)
7:
1760:SchröderâBernstein property
1683:Rathjen's psi function
1419:Kruskal's tree theorem
946:Barwise compactness theorem
857:Regular numerical predicate
629:Mathematical logic journals
10:
2043:
1840:Substructure (mathematics)
1698:Residuated Boolean algebra
1558:Monadic second-order logic
1387:Institutional model theory
1224:Foundations of mathematics
16:The main article for this
15:
2027:Philosophy of mathematics
1649:Proof-theoretic semantics
1575:Non-wellfounded mereology
1301:Grundlagen der Mathematik
1244:FriedbergâMuchnik theorem
397:Logic in computer science
298:Automated theorem proving
1765:Semantic theory of truth
1496:LöwenheimâSkolem theorem
1456:Lindström's theorem
1172:Extension by definitions
1147:Enumeration reducibility
819:Mathematical logic stubs
1775:Semicomputable function
1553:Model-theoretic grammar
1451:Lindenbaum's lemma
1313:Herbrand interpretation
1276:Gödel's ÎČ function
1976:Variable (mathematics)
1959:Universe (mathematics)
1850:Superposition calculus
1639:Proof of impossibility
1518:Mathematical induction
1343:Hypostatic abstraction
1328:Hilbert's program
1219:Formulario mathematico
1152:Equality (mathematics)
1122:Elementary equivalence
1033:Conservative extension
609:Mathematical logicians
2022:Fields of mathematics
1998:Witness (mathematics)
1927:Truth-value semantics
1548:Model complete theory
1239:Free choice inference
1167:Extender (set theory)
1117:Elementary definition
988:Cantor's paradox
929:Algorithmic technique
904:Abstract model theory
434:Forcing (mathematics)
1820:Structural induction
1795:SolĂšr's theorem
1688:Recursive definition
1659:Pure inductive logic
1538:Mivar-based approach
1523:Mathesis universalis
1137:Entscheidungsproblem
1063:Curry's paradox
1038:Continuous predicate
1028:Completeness (logic)
909:Algebraic definition
894:Absoluteness (logic)
862:Computability theory
754:Substitution (logic)
525:Independence results
189:Computability theory
1988:Well-formed formula
1942:Type (model theory)
1932:Turing's proof
1733:Rosser's trick
1708:Reverse mathematics
1481:Logical equivalence
1058:Craig interpolation
1018:Compactness theorem
562:Logical expressions
315:Mathematical axioms
1937:Turnstile (symbol)
1845:Successor function
1770:Semantics of logic
1703:Residuated lattice
1634:Mathematical proof
1466:Löb's theorem
1370:Indicator function
1318:Herbrand structure
1209:Formal calculation
1013:Cointerpretability
998:Categorical theory
852:Mathematical logic
710:Quantifier (logic)
579:Logical positivism
23:Mathematical logic
1993:WFF 'N PROOF
1887:Tautology (logic)
1790:Slicing the Truth
1780:Signature (logic)
1750:S2S (mathematics)
1619:Peirce's law
1436:Law (mathematics)
1296:Ground expression
1199:Finitary relation
1127:Elementary theory
1048:Converse relation
956:Beth definability
380:Categorical logic
2034:
1738:Rules of passage
1693:Relation algebra
1592:O-minimal theory
1471:Outline of logic
1414:Kripke semantics
1392:Interior algebra
1383:
1229:Fragment (logic)
1157:Equational logic
1105:Double turnstile
1080:De Bruijn factor
993:Cartesian monoid
919:Algebraic theory
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451:Formal languages
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48:Recursion theory
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2006:
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2003:
2002:
1980:
1963:
1946:
1922:Truth predicate
1877:Tarski Lectures
1864:
1755:Saturated model
1742:
1675:
1663:
1606:
1584:
1562:
1533:Metamathematics
1510:
1501:LowerUnivalents
1491:ĆoĆâVaught test
1486:Logical machine
1423:
1396:
1379:
1360:Impredicativity
1347:
1305:
1271:Gödel numbering
1253:
1186:
1162:Equiconsistency
1109:
1085:Dedekind number
1072:
1068:Cyclic negation
1023:Complete theory
980:
938:
886:
832:
831:
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829:
826:
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790:
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697:
696:
690:Predicate logic
685:
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636:
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363:Logical calculi
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339:Boolean algebra
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264:Algebraic logic
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1917:Truth function
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1899:
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1884:
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1855:Surreal number
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1446:LĂ©vy hierarchy
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1261:Game semantics
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1214:Formal grammar
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1095:Diagonal lemma
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1043:Contraposition
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1008:Coherent space
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899:Abstract logic
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489:
479:
478:
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468:Formal systems
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391:
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374:
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347:
333:
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329:
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309:
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306:
292:
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275:
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272:
258:
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248:
234:
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231:
217:
216:
214:
200:
199:
197:
183:
182:
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176:
175:
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161:
160:
80:
75:
69:
67:
64:
62:
57:
56:
51:
45:
40:
9:
6:
4:
3:
2:
2039:
2028:
2025:
2023:
2020:
2018:
2015:
2014:
2012:
1999:
1996:
1994:
1991:
1989:
1986:
1985:
1982:
1977:
1974:
1972:
1971:Vacuous truth
1969:
1968:
1965:
1960:
1957:
1955:
1952:
1951:
1948:
1943:
1940:
1938:
1935:
1933:
1930:
1928:
1925:
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1920:
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1684:
1681:
1680:
1677:
1672:
1671:Quantum logic
1669:
1668:
1665:
1660:
1657:
1655:
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1630:
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1625:
1622:
1620:
1617:
1615:
1612:
1611:
1608:
1603:
1602:Ordinal logic
1600:
1598:
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1590:
1589:
1586:
1581:
1578:
1576:
1573:
1571:
1568:
1567:
1564:
1559:
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1541:
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1534:
1531:
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1521:
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1515:
1512:
1507:
1504:
1502:
1499:
1497:
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1492:
1489:
1487:
1484:
1482:
1479:
1477:
1474:
1472:
1469:
1467:
1464:
1462:
1459:
1457:
1454:
1452:
1449:
1447:
1444:
1442:
1439:
1437:
1434:
1432:
1429:
1428:
1425:
1420:
1417:
1415:
1412:
1410:
1407:
1405:
1402:
1401:
1398:
1393:
1390:
1388:
1385:
1382:
1378:
1376:
1375:Infinitesimal
1373:
1371:
1368:
1366:
1363:
1361:
1358:
1356:
1353:
1352:
1349:
1344:
1341:
1339:
1336:
1334:
1331:
1329:
1326:
1324:
1321:
1319:
1316:
1314:
1311:
1310:
1307:
1302:
1299:
1297:
1294:
1292:
1289:
1287:
1284:
1282:
1279:
1277:
1274:
1272:
1269:
1267:
1264:
1262:
1259:
1258:
1255:
1250:
1247:
1245:
1242:
1240:
1237:
1235:
1234:Fraïssé limit
1232:
1230:
1227:
1225:
1222:
1220:
1217:
1215:
1212:
1210:
1207:
1205:
1202:
1200:
1197:
1195:
1192:
1191:
1188:
1183:
1180:
1178:
1175:
1173:
1170:
1168:
1165:
1163:
1160:
1158:
1155:
1153:
1150:
1148:
1145:
1143:
1140:
1138:
1135:
1133:
1132:End extension
1130:
1128:
1125:
1123:
1120:
1118:
1115:
1114:
1111:
1106:
1103:
1101:
1098:
1096:
1093:
1091:
1090:Definable set
1088:
1086:
1083:
1081:
1078:
1077:
1074:
1069:
1066:
1064:
1061:
1059:
1056:
1054:
1051:
1049:
1046:
1044:
1041:
1039:
1036:
1034:
1031:
1029:
1026:
1024:
1021:
1019:
1016:
1014:
1011:
1009:
1006:
1004:
1001:
999:
996:
994:
991:
989:
986:
985:
982:
977:
976:Bunched logic
974:
972:
969:
967:
964:
962:
959:
957:
954:
952:
949:
947:
944:
943:
940:
935:
932:
930:
927:
925:
922:
920:
917:
915:
912:
910:
907:
905:
902:
900:
897:
895:
892:
891:
888:
883:
880:
878:
875:
873:
870:
868:
865:
863:
860:
858:
855:
853:
850:
849:
847:
843:
841:
834:
820:
816:
811:
810:
807:
796:
792:
787:
779:
775:
770:
769:
766:
755:
750:
749:
746:
735:
731:
726:
725:
722:
711:
706:
705:
702:
691:
687:
682:
681:
678:
667:
662:
661:
658:
647:
643:
638:
630:
625:
624:
621:
610:
606:
601:
593:
592:Logical truth
588:
580:
576:
571:
563:
559:
554:
546:
541:
540:
537:
526:
521:
520:
517:
506:
502:
497:
496:
493:
482:
477:
469:
465:
460:
455:(13 C, 201 P)
452:
448:
443:
435:
430:
429:
426:
415:
411:
406:
401:(20 C, 101 P)
398:
394:
389:
381:
377:
372:
364:
360:
355:
354:
351:
340:
336:
331:
330:
327:
316:
312:
307:
299:
295:
290:
285:(59 C, 137 P)
282:
278:
273:
265:
261:
256:
255:
252:
244:(17 C, 155 P)
241:
237:
232:
224:
220:
215:
207:
203:
198:
193:(10 C, 102 P)
190:
186:
181:
180:
177:
173:
169:Subcategories
168:
159:
156:
153:
150:
147:
144:
141:
138:
135:
132:
129:
126:
123:
120:
117:
114:
111:
108:
105:
102:
99:
96:
93:
90:
87:
84:
81:
79:
76:
74:
71:
70:
61:
55:
52:
49:
46:
44:
41:
39:
36:
35:
34:
31:
25:
24:
19:
2017:Formal logic
1954:Ultraproduct
1897:Term algebra
1892:Term (logic)
1800:Special case
1614:Peano axioms
1441:Laws of Form
1333:Hintikka set
877:Proof theory
872:Model theory
837:
823:(2 C, 105 P)
799:(4 C, 113 P)
613:(4 C, 121 P)
343:(2 C, 100 P)
223:Proof theory
210:(3 C, 116 P)
206:Model theory
171:
58:
43:Proof theory
38:Model theory
32:
28:
21:
1723:Ringschluss
1654:Proposition
1629:Prime model
1543:Modal logic
1431:Laver table
1286:Gödel logic
1142:Enumeration
1003:Class logic
795:Type theory
782:(1 C, 54 P)
738:(5 C, 45 P)
694:(2 C, 36 P)
650:(6 C, 50 P)
646:Modal logic
583:(1 C, 20 P)
566:(1 C, 21 P)
509:(1 C, 10 P)
472:(7 C, 10 P)
418:(2 C, 40 P)
367:(4 C, 34 P)
319:(2 C, 22 P)
302:(3 C, 39 P)
268:(1 C, 23 P)
227:(6 C, 95 P)
2011:Categories
1902:Term logic
1835:Subitizing
1338:Hub labels
951:Beta-model
882:Set theory
384:(1 C, 7 P)
281:Algorithms
240:Set theory
54:Set theory
1718:Rewriting
1528:Mereology
924:Algorithm
734:Recursion
66:Contents
1872:T-schema
1194:Finitary
1053:Counting
18:category
1506:Ludics
714:(20 P)
596:(23 P)
529:(21 P)
485:(17 P)
438:(23 P)
1912:Truth
758:(3 P)
670:(5 P)
633:(6 P)
549:(7 P)
78:0â9
73:Top
20:is
2013::
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1983:W
1966:V
1949:U
1867:T
1745:S
1678:R
1666:Q
1609:P
1587:O
1565:N
1513:M
1426:L
1399:K
1350:I
1308:H
1256:G
1189:F
1112:E
1075:D
983:C
941:B
889:A
808:ÎŁ
767:T
747:S
723:R
703:Q
679:P
659:O
622:M
538:L
518:I
494:H
427:F
352:C
328:B
253:A
178:*
158:Z
155:Y
152:X
149:W
146:V
143:U
140:T
137:S
134:R
131:Q
128:P
125:O
122:N
119:M
116:L
113:K
110:J
107:I
104:H
101:G
98:F
95:E
92:D
89:C
86:B
83:A
26:.
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