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.

- "Peano axioms
- "Mathematical induction
- "Naive set theory
- "Universe (mathematics)
- "Axiomatization
- "Axiomatic system
- "Axiomatic method
- "Formal system
- "Mathematical proof
- "Tautology
- "Consistency proof
- "Arithmetization of analysis
- "Foundations of mathematics
- "Formal language
*"Principia Mathematica*- "Hilbert's program
- "Impredicative
- "Definable real number
- "Algebraic logic
- "Dialectica space
- "categorical logic

- "Finite model theory
- "Computable model theory
- "Institutional model theory
- "Non-standard analysis
- "Set theory
- "Kripke semantics
- "Predicate logic
- "Soundness theorem
- "Gödel's completeness theorem
- "Compactness theorem
- "Löwenheim–Skolem theorem
- "Gödel's incompleteness theorems
- "Structure (mathematical logic)
- "Interpretation (logic)
- "Substructure
- "Elementary substructure
- "Non-standard model
- "Atomic model (mathematical logic)
- "Prime model
- "Saturated model
- "Existentially closed model
- "Ultraproduct
- "Age (model theory)
- "Potential isomorphism
- "Theory (mathematical logic)
- "Differentially closed field
- "Exponential field
- "Ax–Grothendieck theorem
- "Ax–Kochen theorem
- "Peano axioms
- "Non-standard model of arithmetic
- "First-order arithmetic
- "Second-order arithmetic
- "Presburger arithmetic
- "Wilkie's theorem
- "Functional predicate
- "T-schema
- "Back-and-forth method
- "Barwise compactness theorem
- "Skolemization
- "Lindenbaum–Tarski algebra
- "Löb's theorem
- "Arithmetical set
- "Definable set
- "Ehrenfeucht–Fraïssé game
- "Herbrand interpretation / "Herbrand structure
- "Imaginary element
- "Indiscernibles
- "Interpretation (model theory) / "Interpretable structure
- "Pregeometry (model theory)
- "Quantifier elimination
- "Reduct
- "Signature (logic)
- "Skolem normal form
- "Type (model theory)
- "Zariski geometry

- "Algebra of sets "
- "Axiom of choice "
- "Boolean algebra (structure)
- "Boolean-valued model "
- "Burali-Forti paradox "
- "Cantor's back-and-forth method
- "Cantor's diagonal argument "
- "Cantor's first uncountability proof "
- "Cantor's theorem "
- "Cantor–Bernstein–Schroeder theorem "
- "Cardinality "
- "Aleph number "
- "Aleph-null
- "Aleph-one "

- "Beth number "
- "Cardinal number "
- "Hartogs number "

- "Aleph number "
- "Cartesian product "
- "Class (set theory) "
- "Complement (set theory) "
- "Complete Boolean algebra "
- "Continuum (set theory) "
- "Continuum hypothesis "
- "Countable set "
- "Descriptive set theory "
- "Determinacy "
- "Empty set "
- "Forcing (mathematics) "
- "Fuzzy set "
- "Internal set theory "
- "Intersection (set theory) "
- "L "
- "L(R) "
- "Large cardinal property "
- "Musical set theory "
- "Ordinal number "
- "Power set "
- "Russell's paradox "
- "Set theory "
- "Set (mathematics) "
- "Simple theorems in the algebra of sets "
- "Subset "
- "Θ (set theory) "
- "Tree (descriptive set theory) "
- "Tree (set theory) "
- "Union (set theory) "
- "Von Neumann universe "
- "Zero sharp "

- "Almost Ramsey cardinal
- "Erdős cardinal
- "Extendible cardinal
- "Huge cardinal
- "Hyper-Woodin cardinal
- "Inaccessible cardinal
- "Ineffable cardinal
- "Mahlo cardinal
- "Measurable cardinal
- "N-huge cardinal
- "Ramsey cardinal
- "Rank-into-rank
- "Remarkable cardinal
- "Shelah cardinal
- "Strong cardinal
- "Strongly inaccessible cardinal
- "Subtle cardinal
- "Supercompact cardinal
- "Superstrong cardinal
- "Totally indescribable cardinal
- "Weakly compact cardinal
- "Weakly hyper-Woodin cardinal
- "Weakly inaccessible cardinal
- "Woodin cardinal
- "Unfoldable cardinal

- "Entscheidungsproblem
- "Decision problem
- "Decidability (logic)
- "Church-Turing thesis
- "Computable function
- "Kleene's recursion theorem
- "Recursively enumerable set
- "Decidable language
- "Undecidable language
- "Rice's theorem
- "Post's theorem
- "Turing degree
- "Effective results in number theory
- "Diophantine set
- "Matiyasevich's theorem
- "Word problem for groups
- "Arithmetical hierarchy
- Subrecursion theory
- "Natural proof
- "Hypercomputation
- "Rózsa Péter
- "Alonzo Church
- "Emil Post
- "Alan Turing
- "Jacques Herbrand
- "Haskell Curry
- "Stephen Cole Kleene
- "Definable real number

- "Metamathematics
- "Cut-elimination
- "Tarski's undefinability theorem
- "Diagonal lemma
- "Provability logic
- "Interpretability logic
- "Sequent
- "Sequent calculus
- "Analytic proof
- "Structural proof theory
- "Self-verifying theories
- "Substructural logics
- "Proof-theoretic semantics
- "Ludics
- "System F
- "Gerhard Gentzen
- "Gentzen's consistency proof
- "Reverse mathematics
- "Nonfirstorderizability
- "Interpretability
- "Weak interpretability
- "Cointerpretability
- "Tolerant sequence
- Cotolerant sequence
- "Deduction theorem
- "Cirquent calculus

- "Nonconstructive proof
- "Existence theorem
- "Intuitionistic logic
- "Intuitionistic type theory
- "Type theory
- "Lambda calculus
- "Simply typed lambda calculus
- "Typed lambda calculus
- "Curry–Howard isomorphism
- "Calculus of constructions
- "Constructivist analysis
- "Lambda cube
- "System F
- "Introduction to topos theory
- "LF (logical framework)
- "Computability logic
- "Computable measure theory
- "Finitism
- "Ultraintuitionism
- "Luitzen Egbertus Jan Brouwer

- "First-order resolution
- "Automated theorem proving
- "ACL2 theorem prover
- "E equational theorem prover
- "Gandalf theorem prover
- "HOL theorem prover
- "Isabelle theorem prover
- "LCF theorem prover
- "Otter theorem prover
- "Paradox theorem prover
- "Vampire theorem prover
- "Interactive proof system
- "Mizar system
- "QED project
- "Coq

*"Begriffsschrift**"Systems of Logic Based on Ordinals*– "Alan Turing's Ph.D. thesis