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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.
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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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This category has the following 17 subcategories, out of 34 total.
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The following 118 pages are in this category, out of 199 total.
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Proof sketch for Gödel's first incompleteness theorem
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952:Reverse Mathematics: Proofs from the Inside Out
234:Large-scale mathematical formalization projects
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33:Mathematical logic is divided into four parts:
594:Implementation of mathematics in set theory
467:Theorems in the foundations of mathematics
1064:Structuralism (philosophy of mathematics)
1024:Simplification of disjunctive antecedents
967:Robinson's joint consistency theorem
534:This list may not reflect recent changes
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562:HilbertâBernays provability conditions
529:Pages in category "Mathematical logic"
1044:List of statements independent of ZFC
1121:Tarski's undefinability theorem
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50:, also known as computability theory
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819:Notre Dame Journal of Formal Logic
715:List of axiomatic systems in logic
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648:König's theorem (set theory)
604:Independence (mathematical logic)
1099:Glossary of mathematical symbols
809:Non-standard model of arithmetic
355:Mathematical logic organizations
1146:Timeline of mathematical logic
1069:Structure (mathematical logic)
863:Predicate (mathematical logic)
643:Knuth's Simpath algorithm
194:Mathematical logic hierarchies
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1054:Strength (mathematical logic)
1049:Stratification (mathematics)
700:Literal (mathematical logic)
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999:SchröderâBernstein property
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318:Mathematical logic journals
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1079:Substructure (mathematics)
937:Residuated Boolean algebra
797:Monadic second-order logic
626:Institutional model theory
16:The main article for this
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1271:Philosophy of mathematics
888:Proof-theoretic semantics
814:Non-wellfounded mereology
1004:Semantic theory of truth
735:LöwenheimâSkolem theorem
695:Lindström's theorem
508:Mathematical logic stubs
1014:Semicomputable function
792:Model-theoretic grammar
690:Lindenbaum's lemma
552:Herbrand interpretation
1215:Variable (mathematics)
1198:Universe (mathematics)
1089:Superposition calculus
878:Proof of impossibility
757:Mathematical induction
582:Hypostatic abstraction
567:Hilbert's program
298:Mathematical logicians
1266:Fields of mathematics
1237:Witness (mathematics)
1166:Truth-value semantics
787:Model complete theory
1059:Structural induction
1034:SolĂšr's theorem
927:Recursive definition
898:Pure inductive logic
777:Mivar-based approach
762:Mathesis universalis
443:Substitution (logic)
214:Independence results
1227:Well-formed formula
1181:Type (model theory)
1171:Turing's proof
972:Rosser's trick
947:Reverse mathematics
720:Logical equivalence
251:Logical expressions
1176:Turnstile (symbol)
1084:Successor function
1009:Semantics of logic
942:Residuated lattice
873:Mathematical proof
705:Löb's theorem
609:Indicator function
557:Herbrand structure
399:Quantifier (logic)
268:Logical positivism
23:Mathematical logic
1232:WFF 'N PROOF
1126:Tautology (logic)
1029:Slicing the Truth
1019:Signature (logic)
989:S2S (mathematics)
858:Peirce's law
675:Law (mathematics)
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977:Rules of passage
932:Relation algebra
831:O-minimal theory
710:Outline of logic
653:Kripke semantics
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841:Ordinal logic
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169:Subcategories
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1261:Formal logic
1193:Ultraproduct
1136:Term algebra
1131:Term (logic)
1039:Special case
853:Peano axioms
680:Laws of Form
572:Hintikka set
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512:(2 C, 105 P)
488:(4 C, 113 P)
302:(4 C, 121 P)
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43:Proof theory
38:Model theory
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962:Ringschluss
893:Proposition
868:Prime model
782:Modal logic
670:Laver table
484:Type theory
471:(1 C, 54 P)
427:(5 C, 45 P)
383:(2 C, 36 P)
339:(6 C, 50 P)
335:Modal logic
272:(1 C, 20 P)
255:(1 C, 21 P)
198:(1 C, 10 P)
1255:Categories
1141:Term logic
1074:Subitizing
577:Hub labels
54:Set theory
957:Rewriting
767:Mereology
423:Recursion
66:Contents
1111:T-schema
18:category
745:Ludics
403:(20 P)
285:(23 P)
218:(21 P)
1151:Truth
447:(3 P)
359:(5 P)
322:(6 P)
238:(7 P)
78:0â9
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