This is a list of mathematical logic topics.
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.
Working foundations
- 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
Model theory
- 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 (mathematics)
- 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
Set theory
- 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
- 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
Descriptive set theory
Large cardinals
- 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
Recursion theory
- 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
Proof theory
- 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
Mathematical constructivism
- 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
Modal logic
Theorem provers
- 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
Discovery systems
Historical
- Begriffsschrift
- Systems of Logic Based on Ordinals – Alan Turing's Ph.D. thesis
See also
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