Logic from A to Z

Abacus machine

Abstract term

Abstraction

Ad hominem argument

Ad ignorantiam argument

Adicity

Adjunction

Affirmative (proposition)

Affirming the consequent, fallacy of

Alephs

Algorithm

Algorithmic function

Alternative denial

Ambiguity, fallacy of

Ampliation

Analytic/synthetic (judgment or proposition)

Ancestral (of a relation)

Antecedent

Antisymmetric relation/order

Apparent variable

Argument

Argument ad hominem

Argument ad ignorantiam

Argument, converse of an

Argument, diagonal

Argument, dialectical

Argument (of a relation/function)

Arity

Asymmetric relation/order

Atomic (sentence or formula)

Automaton

Automorphism

Axiom

Axiom of abstraction

Axiom of choice

Axiom of comprehension

Axiom of constructibility

Axiom of determinateness

Axiom of extensionality

Axiom of foundation

Axiom of infinity

Axiom of pairing

Axiom of power set

Axiom of reducibility

Axiom of regularity

Axiom of replacement

Axiom of separation

Axiom of substitution

Axiom of sumset

Axiom of union

Axiom schema

Axiomatic theory

Axioms, set-theoretic

Bamalip

Bamana

Baralipton

Barbara

Barbari

Baroco

Base component

Base (of propositional operators/connectives)

Begging the question

Bernays-Gödel set theory

Berry's paradox

Beths

Biconditional

Bijection

Bivalence

Bocardo

Bound (occurrence of a) variable

Bound (of a set)

Bramantip

Brouwer's continuity theorem

Burali-Forti's paradox

Calculus

Calemes

Calemop

Calemos

Camene

Camenes

Camenop

Camestres

Camestrop

Cantor's paradox

Cantor's theorem

Cardinal (number)

Cardinality

Cartesian product

Categoremata

Categorical in power

Categorical proposition

Categorical syllogism

Categorical theory

Celantes

Celantop

Celantos

Celarent

Celaro

Celaront

Cesare

Cesaro

Characteristic function

Choice, axiom of

Choice sequence

Choice set/function

Church's theorem

Church's thesis

Church-Turing thesis

Circular reasoning, fallacy of

Class

Class/set distinction

Closure (deductive, logical)

Codomain

Compact cardinal

Compactness

Comparability

Complement

Complete relation/order

Complete set of connectives

Completeness (of a logical calculus)

Completeness (of a theory)

Completeness theorem

Composition, fallacy of

Comprehension

Computable function

Conclusion

Conditional, counterfactual

Conditional, material

Conditional proof

Conjunction

Conjunctive normal form

Connected relation/order

Connotation

Consequent

Consequentiae

Conservative extension (of a theory)

Consistency

Constant

Constant function

Constructibility, axiom of

Constructive choices, principle of

Constructive existence proof

Continuity theorem

Continuous set

Continuum hypothesis

Contraction

Contradiction

Contradiction, law of

Contradictories

Contraposition

Contraries

Contrary to fact conditional

Converse domain

Converse (of an argument)

Converse (of a conditional)

Converse (of a relation)

Conversion per

Conversion, simple

Copula

Countable

Counter domain

Counterfactual (conditional)

Cross product (of sets)

Curry's paradox

Cut-elimination theorems

Dabitis

Darapti

Daraptis

Darii

Datisi

De dicto

De Morgan's laws

De relde dicto

Decidability

Decision problem

Decision procedure

Deducibility

Deduction

Deduction theorem

Degree (of a relation)

Denial

Denotation

Dense relation/order

Denumerable

Denying the antecedent, fallacy of

Derivability conditions

Derivation

Determinateness, axiom of

Dialectical argument

Dilemma

Dilution

Dimaris

Dimatis

Direct product (of sets)

Direct proof

Disamis

Discourse, domain of

Discrete set

Disjunction

Disjunctive normal form

Disjunctive syllogism

Distributed term (of a syllogism)

Division, fallacy of

Domain (of a relation/function)

Domain of discourse

Downward Löwenheim-Skolem theorem

Duality

Effective procedure

Effectively calculable function

Effectively computable function

Elementarily equivalent structures

Empty set

Endomorphism

Enthymeme

Entscheidungsproblem

Epimenides' paradox

Equinumerosity/equipollence

Equivalence class

Equivalence relation

Essentialism

Eubulides' paradox

Ex falso quodlibet

Excluded middle

Exclusive disjunction

Existential generalization

Existential import

Existential instantiation

Extension

Extension (of a theory)

Extensionality, axiom of

Fallacy

Fapesmo

Felapto

Felapton

Ferio

Ferison

Fesapo

Festino

Field (of a relation/function)

Figure (of a categorical syllogism)

Fimeno

Finite

Finite character

First-order/higher-order

Forcing

Formal language

Formal proof

Formal system

Foundation, axiom of

Fraenkel set theory

Free (occurrence of a) variable

Fresison

Frisesomorum

Function

Generalized continuum hypothesis

Gödel sentence

Gödel's theorems

Greatest lower bound

Greatest ordinal, paradox of the

Grelling–Nelson paradox

Grelling's paradox

Halting problem

Hauptsatz

Heap, paradox of the

Henkin sentence

Henkin's problem

Heterologicality, paradox of

Higher-order

Homomorphism

Horned syllogism

Hypothetical syllogism

Identity function

Identity, law of

Identity of indiscernibles

Ignoratio elenchi

Illicit process, fallacy of

Image (of a function)

Immediate inference

Implication, logical

Implication, material

Implication, strict

Impredicative definition

Inaccessible cardinal

Inclusive disjunction

Incompleteness theorems

Inconsistent triad

Indefinite categorical proposition

Independence

Indirect proof

Indiscernibility of identicals

Induction, mathematical

Infimum

Infinite

Infinity, axiom of

Injection

Input (of a function)

Intension

Interpretation

Intersection (of

Into function

Inverse (of a function)

Inverse (of a relation)

Isomorphism

Join

Joint denial

Kleene's second recursion theorem

König's lemma

Large cardinal

Law of comparability

Law of contradiction

Law of (the) excluded middle

Law of identity

Law of trichotomy

Least upper bound

Left field (of a relation)

Lekton

Lemma, König's

Lemma, Zorn's

Liar paradox

Limit ordinal

Limitation of size

Linear relation/order

Löb's theorem

Logical constant

Logical implication

Logistic system

Löwenheim–Skolem theorem(s)

Lower bound

Mahlo cardinal

Major premise (of a syllogism)

Major term (of a syllogism)

Many-valued logics

Mapping (map)

Markov's principle

Material implication

Maximal consistent set

Measurable cardinal

Meet

Middle term (of a syllogism)

Minor premise (of a syllogism)

Minor term (of a syllogism)

Mnemonics, syllogistic

Modal syllogism

Model

Modus ponendo tollens

Modus tollendo ponens

Modus tollens

Mood (of a categorical syllogism)

Multiplicative axiom

Negation

Negation-completeness

Negative (proposition)

Neumann–Bernays–Gödel set theory

Non sequitur

Noncontradiction, law of

Nonstandard model

Normal form (conjunctive)

Normal form (disjunctive)

Normal form (Skolem)

N-tuple

Null set

Obversion

Omega

Omega-completeness

Omega-consistency

Onto function

Open term/formula

Opposition

Order

Ordering

Order type

Ordered n-tuple

Ordered pair

Ordinal (number)

Output (of a function)

Pairing axiom

Paradox, Berry's

Paradox, Burali-Forti's

Paradox, Cantor's

Paradox, Curry's

Paradox, Epimenides'

Paradox of the greatest ordinal

Paradox, Grelling's

Paradox of the heap

Paradox of heterologicality

Paradox, liar

Paradox, Russell's

Paradox, sorites

Paradoxes of material and strict implication

Paralogism

Parameter

Parameter theorem

Parametrization theorem

Partial function

Particular (proposition)

Particular to general reasoning

Partition

Peano postulates (Peano arithmetic)

Petitio principii

Philonian conditional

Polish notation

PolysyUogism

Post completeness

Postulates, Peano

Power (of a set)

Power set

Power set axiom

Predecessor

Predicate

Predicate-functor logic

Predicate logic

Prenex normal form

Pre-ordering

Primitive recursive function

Principle of constructive choices

Problem

Product (of sets)

Projection function

Proof

Proper class

Proposition

Proposition, categorical

Propositional function

Propositional logic

Propositional operator/connective

Provability predicate

Quality (of a categorical proposition)

Quantifier

Quantity (of a categorical proposition)

Quasi-ordering

Ramified theory of types

Range (of a relation/function)

Real variable

Reasoning from particular to general

Recursion theorem

Recursive function

Recursive set

Reducibility, axiom of

Reductio absurdum

Reduction, syllogistic

Reflexive relation/order

Register machine

Regularity, axiom of

Relations (properties of)

Relative complement

Replacement, axiom of

Restriction, axiom of

Richard's paradox

Right field (of a relation)

Rules of inference

Russell's paradox

Satisfaction

Sentence

Separation, axiom of

Sequence

Series

Set/class distinction

Set theory

Set-theoretic axioms

Sheffer stroke

Signature

Signification

Simple relation/order

Simple theory of types

Singular proposition

Skolem theorem

Skolem normal form

S-M-N theorem

Solvable problem

Sophism

Sorites

Soundness (of an argument)

Soundness (of a formal system)

Soundness (of a logical calculus)

Soundness (of a theory)

Square of opposition

Strengthened liar paradox

Strict implication

Structure

Subalternation

Subcontradictories

Subject

Subjunctive conditional

Subset

Substitution, axiom of

Subtheory

Successor

Successor function

Sumset axiom

Superset

Supremum

Surjection

Syllogism

Syllogism, categorical

Syllogism, horned

Syllogism, hypothetical

Syllogism, modal

Symmetric difference of sets

Symmetric relation/order

Syncategoremata

Synthetic (judgment or proposition)

Tarski's undefinability theorem

Tautology, tautological implication

T-equivalence

Tertium non datur

Theorem

Theory, axiomatic

Theory, categorical

Theory, completeness of a

Theory, (conservative) extension of a

Theory, soundness of a

Theory of types

Thinning

Total function

Total relation/order

Transfinite cardinal

Transfinite induction

Transitive closure

Transitive relation/order

Trichotomy

Truth-function

Truth in a model

Truth table

Truth-value

-Tuple

Turing computable function

Turing machine

Types, theory of

Union, axiom of

Union (of sets)

Universal generalization

Universal instantiation

Universal machine theorem

Universal (proposition)

Universal quantifier

Universal set

Universal Turing machine

Upper bound

Upward Löwenheim–Skolem theorem

Validity

Valuation

Value (of a function)

Variable

Vicious-circle principle

Von Neumann–Bernays–Gödel set theory

Weakening

Well-founded relation/order

Well-ordering

Zermelo–Fraenkel set theory

Zorn's lemma