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.
Clicking on related changes shows a list of most-recent edits of articles to which this page links. This page links to itself in order that recent changes to this page will also be included in related changes.
| Contents |
Working foundations
- Peano axioms
- Mathematical induction
- Naive set theory
- Universe (mathematics)
- Axiomatization
- Axiomatic system
- Axiomatic method
- Mathematical proof
- Tautology
- Consistency
- Arithmetization of analysis
- Foundations of mathematics
- Generating arithmetic
- Formal language
- Principia Mathematica
- Hilbert's program
Model theory
- Cantor's back-and-forth method
- Functional predicate, monadic
- First-order predicate calculus
- Lindenbaum-Tarski algebra
- T-schema
- Maximal consistent set
- Compactness theorem
- Löwenheim-Skolem theorem
- Soundness theorem
- Gödel's completeness theorem
- Deduction theorem
- Elementary embedding
- Elementary substructure
- Löb's theorem
- Gödel's incompleteness theorem
- Ultraproduct
- Saturated model
- Non-standard analysis
- Tolerant sequence
- Cotolerant sequence
- Interpretability
- Weak interpretability
- Cointerpretability
- Second-order logic
- Whitehead problem
- Thompson groups
- Kurt Gödel
- Alfred Tarski
- Saharon Shelah
Set theory
- Axiomatic set theory
- Well-founded relation
- Transfinite number
- Ordinal number
- Equinumerous
- Cardinal number
- Cantor-Bernstein-Schroeder theorem
- Zermelo-Fraenkel axioms
- Zermelo set theory
- Von Neumann-Bernays-Gödel axioms
- Class (set theory)
- Continuum hypothesis
- Forcing (mathematics)
- Freiling's axiom of symmetry
- Goodstein's theorem
- Internal set theory
- Gödel's constructible universe
- Von Neumann universe
- Hereditarily finite set
- Normal function
- Covering lemma
- Stratification (mathematics)
- Suslin's problem
- Clubsuit
- Diamondsuit
- Ernst Zermelo
- Paul Cohen
- New Foundations
- Cantor's back-and-forth method
Descriptive set theory
Large cardinals
- Almost Ramsey cardinal
- Erdös cardinal
- Extendible cardinal
- Huge cardinal
- Hyper-Woodin cardinal
- Inaccessible cardinal
- Ineffable cardinal
- Mahlo cardinal
- Measurable cardinal
- N-huge cardinal
- N-Mahlo 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
- Recursive 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
- Alonzo Church
- Emil Post
- Alan Turing
- Jacques Herbrand
- Haskell Curry
- Stephen Cole Kleene
Proof theory
- Metamathematics
- Cut-elimination
- Tarski's indefinability 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
- Reverse mathematics
- Nonfirstorderizability
Mathematical constructivism
- Nonconstructive proof
- Existence theorem
- Intuitionistic logic
- Constructivist analysis
- 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