List of mathematical logic topics

List of mathematical logic topics
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
Giuseppe Peano
Mathematical induction
Structural induction
Recursive definition
Naive set theory
Element (mathematics)
Ur-element
Singleton (mathematics)
Simple theorems in the algebra of sets
Algebra of sets
Power set
Empty set
Non-empty set
Empty function
Universe (mathematics)
Axiomatization
Axiomatic system
Axiom schema
Axiomatic method
Formal system
Mathematical proof
Direct proof
Reductio ad absurdum
Proof by exhaustion
Constructive proof
Nonconstructive proof
Tautology
Consistency proof
Arithmetization of analysis
Foundations of mathematics
Formal language
Principia Mathematica
Hilbert's program
Impredicative
Definable real number
Algebraic logic
Boolean algebra (logic)
Dialectica space
categorical logic
Model theory
Finite model theory
Descriptive complexity theory
Model checking
Trakhtenbrot's theorem
Computable model theory
Tarski's exponential function problem
Undecidable problem
Institutional model theory
Institution (computer science)
Non-standard analysis
Non-standard calculus
Hyperinteger
Hyperreal number
Transfer principle
Overspill
Elementary Calculus: An Infinitesimal Approach
Criticism of non-standard analysis
Standard part function
Set theory
Forcing (mathematics)
Boolean-valued model
Kripke semantics
General frame
Predicate logic
First-order logic
Infinitary logic
Many-sorted logic
Higher-order logic
Lindström quantifier
Second-order logic
Soundness theorem
Gödel's completeness theorem
Original proof of Gödel's completeness theorem
Compactness theorem
Löwenheim–Skolem theorem
Skolem's paradox
Gödel's incompleteness theorems
Structure (mathematical logic)
Interpretation (logic)
Substructure (mathematics)
Elementary substructure
Skolem hull
Non-standard model
Atomic model (mathematical logic)
Prime model
Saturated model
Existentially closed model
Ultraproduct
Age (model theory)
Amalgamation property
Hrushovski construction
Potential isomorphism
Theory (mathematical logic)
Complete theory
Vaught's test
Morley's categoricity theorem
Stability spectrum
Morley rank
Stable theory
Forking extension
Strongly minimal theory
Stable group
Tame group
o-minimal theory
Weakly o-minimal structure
C-minimal theory
Spectrum of a theory
Vaught conjecture
Model complete theory
List of first-order theories
Conservative extension
Elementary class
Pseudoelementary class
Strength (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
Axiom of countable choice
Axiom of dependent choice
Zorn's lemma
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
Cartesian product
Class (set theory)
Complement (set theory)
Complete Boolean algebra
Continuum (set theory)
Suslin's problem
Continuum hypothesis
Countable set
Descriptive set theory
Analytic set
Analytical hierarchy
Borel equivalence relation
Infinity-Borel set
Lightface analytic game
Perfect set property
Polish space
Prewellordering
Projective set
Property of Baire
Uniformization (set theory)
Universally measurable set
Determinacy
AD+
Axiom of determinacy
Axiom of projective determinacy
Axiom of real determinacy
Empty set
Forcing (mathematics)
Fuzzy set
Internal set theory
Intersection (set theory)
L
L(R)
Large cardinal property
Musical set theory
Ordinal number
Infinite descending chain
Limit ordinal
Successor ordinal
Transfinite induction
∈-induction
Well-founded set
Well-order
Power set
Russell's paradox
Set theory
Alternative set theory
Axiomatic set theory
Kripke–Platek set theory with urelements
Morse–Kelley set theory
Naive set theory
New Foundations
Positive set theory
Zermelo–Fraenkel set theory
Zermelo 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
Analytical hierarchy
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
Algorithm
Recursion
Primitive recursive function
Mu operator
Ackermann function
Turing machine
Halting problem
Computability theory, computation
Herbrand Universe
Markov algorithm
Lambda calculus
Church-Rosser theorem
Calculus of constructions
Combinatory logic
Post correspondence problem
Kleene's recursion theorem
Recursively enumerable set
Recursively enumerable language
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
Presburger arithmetic
Computational complexity theory
Polynomial time
Exponential time
Complexity class
Complexity classes P and NP
Cook's theorem
List of complexity classes
Polynomial hierarchy
Exponential hierarchy
NP-complete
Time hierarchy theorem
Space hierarchy theorem
Natural proof
Hypercomputation
Oracle machine
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
Structural rule
Weakening
Contraction
Linear logic
Intuitionistic linear logic
Proof net
Affine logic
Strict logic
Relevant logic
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
Church–Rosser theorem
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
Kripke semantics
Sahlqvist formula
Interior algebra
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
Automated Mathematician
Eurisko
Historical
Begriffsschrift
Systems of Logic Based on Ordinals – Alan Turing's Ph.D. thesis
See also
Kurt Gödel
Alfred Tarski
Saharon Shelah
Logic
L
Mathematical logic
Mathematical logic
Mathematical logic