A

• Adjoint functorsRelationship between two functors abstracting many common constructions
• Aleph numberInfinite cardinal number
• Arrow (symbol)Graphical symbol or pictogram used to point or indicate direction
• Atomic formulaMathematical logic concept
• Axiom of extensionalityAxiom used in set theory
• Axiom of infinityAxiom of Zermelo-Fraenkel set theory
• Axiom of pairingConcept in axiomatic set theory
• Axiom of power setConcept in axiomatic set theory
• Axiom of regularityAxiom of set theory
• Axiom of unionConcept in axiomatic set theory
• Axiom schema of replacementConcept in set theory
• Axiom schema of specificationConcept in axiomatic set theory
• Axiomatic systemMathematical term; concerning axioms used to derive theorems

B

• Banach–Tarski paradoxTheorem in set-theoretic geometry
• Biconditional eliminationBiconditional elimination is the name of two valid rules of inference of propositional log
• Biconditional introductionIn propositional logic, biconditional introduction is a valid rule of inference. It allows
• Bidirectional trafficIn transportation infrastructure, a bidirectional traffic system divides travellers into t
• Binary relationRelationship between elements of two sets
• Brouwer–Heyting–Kolmogorov interpretationInterpretation of intuitionistic logic

C

• Cantor's diagonal argumentProof in set theory
• Cantor's theoremEvery set is smaller than its power set
• Cardinal numberSize of a possibly infinite set
• Cardinality of the continuumCardinality of the set of real numbers
• Cartesian closed categoryType of category in category theory
• Cartesian productMathematical set formed from two given sets
• Category (mathematics)Collection of objects and morphisms
• Church–Turing thesisThesis on the nature of computability
• Church's thesis (constructive mathematics)In constructive mathematics, Church's thesis is the principle stating that all total funct
• CircumlocutionCircumlocution (also called circumduction, circumvolution, periphrasis, kenning, or ambage
• Class (set theory)Collection of sets in mathematics that can be defined based on a property of its members
• Closure (mathematics)Operation on the subsets of a set
• Combinatory logicLogical formalism using combinators instead of variables
• Comma categoryIn mathematics, a comma category (a special case being a slice category) is a construction
• Commutative diagramCollection of maps which give the same result
• Compactness theoremTheorem in mathematical logic
• Complement (set theory)Set of the elements not in a given subset
• Computable setSet with algorithmic membership test
• Computably enumerable setMathematical logic concept
• Concrete categoryCategory equipped with a faithful functor to the category of sets
• Conjunction eliminationIn propositional logic, conjunction elimination (also called and elimination, ∧ eliminatio
• Continuum hypothesisProposition in mathematical logic
• ContrapositionMathematical logic concept
• Converse nonimplicationLogical connective
• CoproductCategory-theoretic construction

D

• De Morgan's lawsPair of logical equivalences
• Decision problemYes/no problem in computer science
• Disjunction introductionDisjunction introduction or addition (also called or introduction) is a rule of inference
• Disjunctive syllogismLogical rule of inference
• Double negationPropositional logic theorem

E

• Element (category theory)In category theory, the concept of an element, or a point, generalizes the more usual set
• Element of a setAny one of the distinct objects that make up a set in set theory
• Elementary equivalenceConcept in model theory
• EntscheidungsproblemImpossible task in computing
• Epsilon-inductionIn set theory, -induction, also called epsilon-induction or set-induction, is a principle
• Equivalence classMathematical concept
• Equivalence class (music)In music theory, equivalence class is an equality (=) or equivalence between properties of
• Event structureIn mathematics and computer science, an event structure describes sequences of events that
• Existential quantificationMathematical use of "there exists"
• Exportation (logic)Rule of replacement in propositional logic

F

• Five lemmaLemma in category theory about commutative diagrams
• Forcing (computability)Forcing in computability theory is a modification of Paul Cohen's original set-theoretic t
• Forcing (mathematics)Technique for proving independence results
• Forgetful functorConcept in category theory
• Foundations of mathematicsBasic framework of mathematics
• Free latticeIn mathematics, in the area of order theory, a free lattice is the free object correspondi
• Free objectLeft adjoint to a forgetful functor to sets
• Free variables and bound variablesConcept in mathematics or computer science
• FunctorMapping between categories
• Functor categoryIn category theory, a branch of mathematics, a functor category is a category where the ob

G

• General recursive functionOne of several equivalent definitions of a computable function
• Generic filterIn the mathematical field of set theory, a generic filter is a kind of object used in the
• Gisbert HasenjaegerGisbert F. R. Hasenjaeger (1 June 1919 – 2 September 2006) was a German mathematical logic
• Gödel numberingFunction in mathematical logic
• Gödel's completeness theoremFundamental theorem in mathematical logic
• Ground expressionTerm that does not contain any variables

H

• Halting problemProblem in computer science
• Hereditary setIn set theory, a hereditary set (or pure set) is a set whose elements are all hereditary s
• Higher-order logicFormal system of logic
• Hilbert's axiomsBasis for Euclidean geometry
• Hom functorFunctor mapping hom objects to an underlying category

I

• If and only ifLogical connective
• ImpredicativityIn mathematics, logic and philosophy of mathematics, something that is impredicative is a
• Independence (mathematical logic)Term in mathematical logic
• Infinite regressPhilosophical problem
• Initial and terminal objectsSpecial objects used in (mathematical) category theory
• IntuitionismApproach in philosophy of mathematics and logic
• Intuitionistic logicVarious systems of symbolic logic

J

• John PettieJohn Pettie RA (17 March 1839 – 21 February 1893) was a painter from Edinburgh who spent m

K

• Karnaugh mapGraphical method to simplify Boolean expressions

L

• Lambda calculusMathematical-logic system
• Large cardinalSet theory concept
• Leopold LöwenheimLeopold Löwenheim [ˈle:o:pɔl̩d ˈlø:vɛnhaɪm] (26 June 1878 in Krefeld – 5 May 1957 in Berli
• Limit (category theory)Mathematical concept
• Local variableComputer programming, a variable only usable in a portion of a program (the scope)
• Logical biconditionalIf and only if relation
• Logical connectiveSymbol connecting formulas in logic
• Logical disjunctionLogical connective OR
• Logical NORBinary operation that is true if and only if both operands are false
• Löwenheim–Skolem theoremExistence and cardinality of models of logical theories

M

• Material conditionalLogical connective
• Material nonimplicationLogical connective
• Mathematical structureAdditional mathematical object
• Maurice KarnaughMaurice Karnaugh (; October 4, 1924 – November 8, 2022) was an American physicist, mathema
• Model of computationMathematical model describing how an output of a function is computed given an input
• Model theoryArea of mathematical logic
• Modus ponensRule of logical inference
• Modus tollensRule of logical inference
• MorphismMap (arrow) between two objects of a category
• Mu operatorConcept in computability theory
• MultisetMathematical set with repetitions allowed

N

• Natural transformationCentral object of study in category theory
• NegationLogical operation
• New FoundationsAxiomatic set theory devised by W.V.O. Quine
• NIMPLY gateThe NIMPLY gate is a digital logic gate that implements a material nonimplication.

O

• ObfuscationUnclear communication
• Opposite categoryMathematical category formed by reversing morphisms
• Oracle machineAbstract machine used to study decision problems
• Ordered pairPair of mathematical objects
• Ordinal arithmeticIn the mathematical field of set theory, ordinal arithmetic describes the three usual oper
• Ordinal numberGeneralization of "n-th" to infinite cases

P

• Partition of a setMathematical ways to group elements of a set
• Peano axiomsAxioms for the natural numbers
• Polish notationMathematics notation with operators preceding operands
• Post's latticeIn logic and universal algebra, Post's lattice denotes the lattice of all clones on a two-
• Power setMathematical set of all subsets of a set
• Prenex normal formFormalism of first-order logic
• Primitive recursive functionFunction computable with bounded loops
• Principle of explosionTheorem in formal logic
• Product (category theory)Generalized object in category theory
• Product categoryIn the mathematical field of category theory, the product of two categories C and D, denot
• Proof by contrapositiveIn logic, the contrapositive of a conditional statement is formed by negating both terms a
• Proof theoryBranch of mathematical logic
• Propositional variableIn mathematical logic, a propositional variable (also called a sentence letter, sentential

Q

• Quantifier (logic)Mathematical use of "for all" and "there exists"
• Quantifier eliminationSimplification technique in mathematical logic
• Quotient categoryIn mathematics, a quotient category is a category obtained from another category by identi

R

• Reductio ad absurdumArgument that leads to a logical absurdity
• Reflexive relationBinary relation that relates every element to itself
• Rice's theoremTheorem in computability theory
• Rule of inferenceMethod of deriving conclusions
• Rule of replacementInference rule that may be applied to only a particular segment of an expression

S

• Scope (logic)Range of application for a quantifier or connective in a logical formula
• Second-order logicForm of logic that allows quantification over predicates
• Sentence (mathematical logic)In mathematical logic, a sentence (or closed formula) of a predicate logic is a Boolean-va
• Sheffer strokeLogical operation
• Signature (logic)Description of non-logical symbols
• Skolem normal formFormalism of first-order logic
• Skolem–Noether theoremIn ring theory, a branch of mathematics, the Skolem–Noether theorem characterizes the auto
• Skolem's paradoxMathematical logic concept
• Snake lemmaTheorem in homological algebra
• Space (mathematics)Mathematical set with some added structure
• Structural proof theoryIn mathematical logic, structural proof theory is the subdiscipline of proof theory that s
• Structure (mathematical logic)Mapping of mathematical formulas to a particular meaning
• SubcategoryCategory whose objects and morphisms are inside a bigger category
• Substitution (logic)Concept in logic
• Symmetric relationType of binary relation

T

• Tarski's axiomsAxiom set used in first-order logic
• Tautology (logic)In logic, a statement which is always true
• Tautology (rule of inference)In propositional logic, tautology is either of two commonly used rules of replacement. The
• Tee (symbol)The tee (⊤, \top in LaTeX), also called down tack (as opposed to the up tack) or verum, is
• Theory (mathematical logic)Set of sentences in a formal language
• Thoralf SkolemNorwegian mathematician
• Transfinite inductionMathematical concept
• Transitive relationType of binary relation
• Transposition (logic)In propositional logic, transposition is a valid rule of replacement that permits one to s
• Truth functionFunction in logic
• Truth tableMathematical table used in logic
• TupleFinite ordered list of elements
• Turing degreeMeasure of unsolvability
• Turing machineComputation model defining an abstract machine
• Turing reductionConcept in computability theory
• Turing's proofProof by Alan Turing
• Type (model theory)Concept in model theory
• Type theoryMathematical theory of data types

U

• UltraproductMathematical construction
• Undecidable problemYes-or-no question that cannot ever be solved by a computer
• Universal generalizationRule of inference in predicate logic
• Universal instantiationIn predicate logic, universal instantiation (UI; also called universal specification or un
• Universal propertyCharacterizing property of mathematical constructions
• Universal quantificationMathematical use of "for all"
• Universal setMathematical set containing all objects
• Universal Turing machineType of Turing machine
• Universe (mathematics)All-encompassing set or class

V

• Vertical barTypographic symbol
• Von Neumann universeSet theory concept

W

• Well-formed formulaSyntactically correct logical formula
• Well-ordering theoremTheorem that every set can be well-ordered

Y

• Yoneda lemmaEmbedding of categories into functor categories

Z

• Zermelo–Fraenkel set theoryStandard system of axiomatic set theory
• Zorn's lemmaMathematical proposition equivalent to the axiom of choice