List of mathematical logic topics
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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
[edit]- 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
[edit]- 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
[edit]- 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
[edit]Large cardinals
[edit]- 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
[edit]- 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
[edit]- 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
[edit]- 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
[edit]Theorem provers
[edit]- 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
[edit]Historical
[edit]- Begriffsschrift
- Systems of Logic Based on Ordinals – Alan Turing's Ph.D. thesis
See also
[edit]
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