List of mathematical logic topics

This is a list of mathematical logic topics, by Wikipedia page.

For traditional syllogistic logic, see the list of topics in logic. See also the list of computability and complexity topics for more theory of algorithms.

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Table of contents

1 Working foundations 2 Model theory 3 Set theory 4 Large cardinals 5 Recursion theory 6 Proof theory 7 Mathematical constructivism

Working foundations

• Peano axioms
• Mathematical induction
  • Three forms of mathematical induction
  • Structural induction
• Naive set theory
  • Simple theorems in set theory
  • Power set
  • Empty set
  • Empty function
• Universe (mathematics)
• Axiomatization
• Axiomatic system
• Mathematical proof
• Tautology
• Consistency
• Arithmetization of analysis
• Foundations of mathematics
• Generating arithmetic
• Formal language
• Giuseppe Peano

Model theory

• Functional predicate
• First-order predicate calculus
• Compactness theorem
• Löwenheim-Skolem theorem
• Soundness theorem
• Gödel's completeness theorem
  • Original proof of Gödel's completeness theorem
• Gödel's incompleteness theorem
• Ultraproduct
• Non-standard analysis
  • Hyperreal number
• Second-order logic
• Whitehead problem
• Kurt Gödel
• Alfred Tarski
• Saharon Shelah

Set theory

• Axiomatic set theory
• Well-founded relation
• Transfinite number
  • Hilbert's paradox of the Grand Hotel
• Ordinal number
  • Burali-Forti paradox
  • Limit ordinal
• Cardinal number
  • Countable set
  • Uncountable
  • Cantor's first uncountability proof
  • Cantor's diagonal argument
  • Cantor's theorem
  • König's theorem
  • Aleph number
  • 2 to the power of C
  • Regular cardinal
  • Limit cardinal
  • Zero sharp
• Cantor-Bernstein-Schroeder theorem
• Zermelo-Fraenkel axioms
  • Axiom of regularity
  • Axiom of extensionality
  • Axiom of pairing
  • Axiom of empty set
  • Axiom of power set
  • Axiom of union
  • Axiom of infinity
  • Axiom schema of specification
  • Axiom schema of replacement
  • Axiom of choice
    • Zorn's lemma
    • Well ordering theorem
    • Well-ordering principle
    • Transfinite induction
    • Hausdorff maximality theorem
    • Axiom of dependent choice
    • Boolean prime ideal theorem
    • Ultrafilter lemma
• Zermelo set theory
• Class (set theory)
• Continuum hypothesis
• Forcing (mathematics)
• Freiling's Axiom of Symmetry
• Goodstein's theorem
• Gödel's constructible universe
• Hereditarily finite set
• Suslin's problem
• Ernst Zermelo
• Paul Cohen

Large cardinals

• Erdös cardinal
• Extendible cardinal
• Huge cardinal
• Inaccessible cardinal
• Ineffable cardinal
• Mahlo cardinal
• Measurable cardinal
• N-huge cardinal
• N-Mahlo cardinal
• Ramsey cardinal
• Rank-into-rank
• Strong cardinal
• Strongly inaccessible cardinal
• Subtle cardinal
• Supercompact cardinal
• Superstrong cardinal
• Totally indescribable cardinal
• Weakly compact cardinal
• Weakly inaccessible cardinal
• Woodin cardinal

Recursion theory

• Entscheidungsproblem
• Decision problem
• Church-Turing thesis
• Recursive function
  • Algorithm
  • Recursion
  • Primitive recursive function
  • Ackermann function
  • Turing machine
  • Halting problem
  • Computability theory, computation
  • Herbrand Universe
  • Markov algorithm
  • Lambda calculus
    • Church-Rosser theorem
  • Combinatory logic
  • Post correspondence problem
• Kleene's recursion theorem
• Recursively enumerable set
  • Recursively enumerable language
• Decidable language
• Undecidable language
• Rice's theorem
• Effective results in number theory
• Diophantine set
• Matiyasevich's theorem
• Arithmetical hierarchy
• Subrecursion theory
  • Presburger arithmetic
  • Computational complexity theory
  • Polynomial time
  • Exponential time
  • Complexity classes P and NP
  • NP-complete
• Hypercomputation
  • Oracle machine
• Alonzo Church
• Emil Post
• Alan Turing
• Jacques Herbrand
• Haskell Curry
• Stephen Cole Kleene

Proof theory

• Metamathematics
• Sequent
• Sequent calculus
• Substructural logics
  • Relevant logic
• Gerhard Gentzen

Mathematical constructivism

• Nonconstructive proof
• Intuitionistic logic
  • Type theory
  • Introduction to topos theory
• Constructivist analysis
• Finitism
• Ultraintuitionism
• Luitzen Egbertus Jan Brouwer