# ⓘ List of mathematical logic topics

## ⓘ 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.

## 1. Working foundations

• Giuseppe Peano
• Peano axioms
• Recursive definition
• Mathematical induction
• Structural induction
• Element mathematics
• Ur-element
• Naive set theory
• Empty function
• Power set
• Simple theorems in the algebra of sets
• Non-empty set
• Empty set
• Algebra of sets
• Singleton mathematics
• Axiom schema
• Axiomatization
• Axiomatic system
• Universe mathematics
• Nonconstructive proof
• Mathematical proof
• Reductio ad absurdum
• Axiomatic method
• Constructive proof
• Formal system
• Direct proof
• Proof by exhaustion
• Formal language
• Foundations of mathematics
• Arithmetization of analysis
• Principia Mathematica
• Algebraic logic
• Impredicative
• Definable real number
• Consistency proof
• Tautology
• Boolean algebra logic
• Hilberts program
• categorical logic
• Dialectica space

## 2. Model theory

• Finite model theory
• Model checking
• Descriptive complexity theory
• Trakhtenbrots theorem
• Undecidable problem
• Tarskis exponential function problem
• Computable model theory
• Institution computer science
• Institutional model theory
• Hyperinteger
• Overspill
• Criticism of non-standard analysis
• Non-standard analysis
• Transfer principle
• Standard part function
• Elementary Calculus: An Infinitesimal Approach
• Non-standard calculus
• Hyperreal number
• Boolean-valued model
• Set theory
• Forcing mathematics
• General frame
• Kripke semantics
• Predicate logic
• Infinitary logic
• First-order logic
• Many-sorted logic
• Lindstrom quantifier
• Higher-order logic
• Second-order logic
• Original proof of Godels completeness theorem
• Soundness theorem
• Godels completeness theorem
• Skolems paradox
• Compactness theorem
• Lowenheim–Skolem theorem
• Substructure mathematics
• Skolem hull
• Structure mathematical logic
• Elementary substructure
• Godels incompleteness theorems
• Interpretation logic
• Hrushovski construction
• Ultraproduct
• Saturated model
• Non-standard model
• Age model theory
• Atomic model mathematical logic
• Amalgamation property
• Prime model
• Existentially closed model
• Theory mathematical logic
• Potential isomorphism
• Vaughts test
• Complete theory
• Morley rank
• Stable group
• Forking extension
• Tame group
• Morleys categoricity theorem
• Strongly minimal theory
• Stable theory
• Stability spectrum
• Weakly o-minimal structure
• o-minimal theory
• Spectrum of a theory
• C-minimal theory
• Vaught conjecture
• Model complete theory
• Pseudoelementary class
• Elementary class
• List of first-order theories
• Strength mathematical logic
• Conservative extension
• Ax–Kochen theorem
• Non-standard model of arithmetic
• Herbrand interpretation / Herbrand structure
• Pregeometry model theory
• Wilkies theorem
• Type model theory
• Signature logic
• Arithmetical set
• Ehrenfeucht–Fraïsse game
• Barwise compactness theorem
• Peano axioms
• Functional predicate
• Skolemization
• Differentially closed field
• Skolem normal form
• Lobs theorem
• T-schema
• First-order arithmetic
• Presburger arithmetic
• Reduct
• Definable set
• Interpretation model theory / Interpretable structure
• Quantifier elimination
• Back-and-forth method
• Indiscernibles
• Second-order arithmetic
• Imaginary element
• Lindenbaum–Tarski algebra
• Ax–Grothendieck theorem
• Exponential field
• Zariski geometry

## 3. Set theory

• Axiom of choice
• Axiom of countable choice
• Axiom of dependent choice
• Zorns lemma
• Algebra of sets
• Cantors diagonal argument
• Cantors back-and-forth method
• Aleph-null
• Cardinality
• Boolean algebra structure
• Burali-Forti paradox
• Aleph-one
• Cantors first uncountability proof
• Boolean-valued model
• Cantors theorem
• Cantor–Bernstein–Schroeder theorem
• Aleph number
• Beth number
• Cardinal number
• Hartogs number
• Complement set theory
• Continuum set theory
• Suslins problem
• Class set theory
• Cartesian product
• Complete Boolean algebra
• Uniformization set theory
• Perfect set property
• Prewellordering
• Infinity-Borel set
• Borel equivalence relation
• Countable set
• Continuum hypothesis
• Property of Baire
• Universally measurable set
• Analytical hierarchy
• Projective set
• Descriptive set theory
• Polish space
• Lightface analytic game
• Analytic set
• Determinacy
• AD+
• Axiom of determinacy
• Axiom of projective determinacy
• Axiom of real determinacy
• LR
• Intersection set theory
• ∈-induction
• Empty set
• Ordinal number
• Large cardinal property
• Musical set theory
• Successor ordinal
• Limit ordinal
• Infinite descending chain
• L
• Fuzzy set
• Forcing mathematics
• Transfinite induction
• Internal set theory
• Well-order
• Well-founded set
• Kripke–Platek set theory with urelements
• New Foundations
• Naive set theory
• Positive set theory
• Set theory
• Axiomatic set theory
• Zermelo–Fraenkel set theory
• Alternative set theory
• Morse–Kelley set theory
• Power set
• Zermelo set theory
• Russells paradox
• Set mathematics
• Θ set theory
• Subset
• Tree set theory
• Tree descriptive set theory
• Von Neumann universe
• Union set theory
• Simple theorems in the algebra of sets
• Zero sharp

## 4. Large cardinals

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

## 5. Recursion theory

• Primitive recursive function
• Decision problem
• Ackermann function
• Church-Rosser theorem
• Herbrand Universe
• Mu operator
• Halting problem
• Entscheidungsproblem
• Computability theory, computation
• Recursion
• Calculus of constructions
• Markov algorithm
• Lambda calculus
• Church-Turing thesis
• Turing machine
• Algorithm
• Computable function
• Decidability logic
• Post correspondence problem
• Combinatory logic
• Kleenes recursion theorem
• Recursively enumerable language
• Recursively enumerable set
• Diophantine set
• Effective results in number theory
• Arithmetical hierarchy
• Computational complexity theory
• Polynomial hierarchy
• Rices theorem
• Exponential time
• Undecidable language
• Decidable language
• Word problem for groups
• Subrecursion theory
• Exponential hierarchy
• Posts theorem
• Turing degree
• Complexity class
• Matiyasevichs theorem
• Polynomial time
• Presburger arithmetic
• Cooks theorem
• Complexity classes P and NP
• List of complexity classes
• NP-complete
• Space hierarchy theorem
• Time hierarchy theorem
• Natural proof
• Oracle machine
• Hypercomputation
• Alonzo Church
• Haskell Curry
• Stephen Cole Kleene
• Definable real number
• Emil Post
• Alan Turing
• Jacques Herbrand
• Rozsa Peter

## 6. Proof theory

• Contraction
• Sequent
• Tarskis undefinability theorem
• Structural rule
• Cut-elimination
• Diagonal lemma
• Sequent calculus
• Structural proof theory
• Substructural logics
• Self-verifying theories
• Metamathematics
• Interpretability logic
• Provability logic
• Analytic proof
• Weakening
• Proof net
• Linear logic
• Intuitionistic linear logic
• Relevant logic
• Affine logic
• Strict logic
• Cotolerant sequence
• System F
• Reverse mathematics
• Nonfirstorderizability
• Gentzens consistency proof
• Gerhard Gentzen
• Tolerant sequence
• Deduction theorem
• Cirquent calculus
• Ludics
• Weak interpretability
• Proof-theoretic semantics
• Cointerpretability
• Interpretability

## 7. Mathematical constructivism

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

## 8. Theorem provers

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

• feature of this field is the use of formal languages to express the ideas whose logical validity is being studied. List of mathematical logic topics Logical
• Lists of mathematics topics cover a variety of topics related to mathematics Some of these lists link to hundreds of articles some link only to a few
• Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics It bears close connections to metamathematics
• theory Analysis Foundations of mathematics Philosophy of mathematics Category theory Set theory Type theory Mathematical logic Model theory Proof theory
• Computation - - Journal of Mathematical Logic - - Journal of Philosophical Logic - - Journal of Symbolic Logic - - Judgment mathematical logic - - Judgmental language
• matters, see the list of mathematical logic topics See also list of algorithms, list of algorithm general topics Lookup table Mathematical table Multiplication
• complete list of mathematical terms just a selection of typical terms of art that may be encountered. Logic a study of reasoning Set theory a study of collections
• This is a list of topics around Boolean algebra and propositional logic Algebra of sets Boolean algebra structure Boolean algebra Field of sets Logical
• notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language. Mathematical logic is an extension of symbolic