blanketglossary

Transfinite induction

Definition

Transfinite induction is an extension of mathematical induction to well-ordered sets, for example to sets of ordinal numbers or cardinal numbers. Its correctness is a theorem of ZFC.

Related concepts

Abraham Fraenkel Abstract logic Ackermann set theory Aleph number Algebraic logic Almost Alphabet (formal languages)Alternative set theory Amorphous set Argument Arity Atomic formula Atomic model (mathematical logic)Atomic sentence Automata theory Automated theorem proving Axiom Axiom of adjunction Axiom of choice Axiom of constructibility Axiom of countable choice Axiom of dependent choice Axiom of determinacy Axiom of extensionality Axiom of global choice Axiom of infinity Axiom of limitation of size Axiom of pairing Axiom of power set Axiom of projective determinacy Axiom of regularity Axiom of union Axiom schema Axiom schema of replacement Axiom schema of specification Axiomatic system Axiomatization of Boolean algebras Banach–Tarski paradox Basis (vector space)Bertrand Russell Bijection Binary operation Binary relation Boolean algebra Boolean algebras canonically defined Boolean function Borel sets Burali-Forti paradox Cantor's diagonal argument Cantor's paradox Cantor's theorem Cardinal number Cardinality Cardinality of the continuum Cartesian product Categorical theory Category (mathematics)Category of sets Category theory Church encoding Church–Turing thesis Class (set theory)Classical logic Codomain Compactness theorem Complement (set theory)Complete theory Computability theory Computable function Computable set Computably enumerable set Concrete category Conservative extension Consistency Constructible universe Construction of the real numbers Constructive set theory Continuum hypothesis Countable set De Morgan's laws Decidability (logic)Decision problem Dedekind-infinite set Deductive system Diagram (mathematical logic)Disjoint union Domain of a function Dover Publications Element (mathematics)Elementary diagram Elementary equivalence Elementary function arithmetic Empty set Enumeration Epsilon-induction Equiconsistency Equivalence relation Eric W. Weisstein Ernst Zermelo Euclid's Elements Euclidean geometry Existential quantification Expression (mathematics)Extension by definitions Extension by new constant and function names Extensionality Family of sets Filter on a set Finitary relation Finite-valued logic Finite model theory Finite set First-order logic Fixed-point logic Forcing (mathematics)Formal grammar Formal language Formal proof Formal semantics (logic)Formal system Formation rule Foundations of geometry Foundations of mathematics Free logic Free variables and bound variables Function (mathematics)Functional predicate Fuzzy set General set theory Georg Cantor Grothendieck universe Ground expression Ground formula Gödel's completeness theorem Gödel's incompleteness theorems Gödel numbering Halting problem Hereditarily finite set Hereditary set Higher-order logic Hilbert's axioms Hilbert system History of logic History of mathematical logic Image (mathematics)Inaccessible cardinal Independence (mathematical logic)Inference Infinite-valued logic Infinite set Information theory Inhabited set Injective function Interpretation (logic)Interpretation (model theory)Interpretation function Intersection (set theory)Isomorphism John von Neumann Jonathan Emerson Kolmogorov complexity Kripke's theory of truth Kripke–Platek set theory Kurt Gödel Lambda calculus Large cardinal Lemma (mathematics)Limit ordinal Lindström's theorem Linear span List of Hilbert systems List of axioms List of first-order theories List of formal systems List of mathematical theories List of set identities and relations List of statements independent of ZFC Logic Logical biconditional Logical conjunction Logical connective Logical consequence Logical constant Logical disjunction Logical equality Logical equivalence Logical truth Logicism Löwenheim–Skolem theorem Many-valued logic Map (mathematics)Mark Lezama Martin's axiom Material conditional MathWorld Mathematical induction Mathematical logic Mathematical object Metalanguage Minimal axioms for Boolean algebra Model complete theory Model theory Monadic predicate calculus Monadic second-order logic Morse–Kelley set theory NP (complexity)Naive set theory Natural deduction Negation New Foundations Non-Euclidean geometry Non-logical symbol Non-standard model Non-standard model of arithmetic Open formula Operation (mathematics)Ordered pair Ordinal analysis Ordinal number P (complexity)P versus NP problem Paradoxes of set theory Partition of a set Patrick Suppes Paul Bernays Paul Cohen Peano axioms Philosophy of mathematics Power set Predicate (mathematical logic)Predicate logic Predicate variable Prime model Primitive recursive arithmetic Primitive recursive function Principia Mathematica Proof of impossibility Proof theory Proper class Property (mathematics)Proposition Propositional calculus Propositional formula Propositional variable Quantifier (logic)Quantifier rank Rational number Real number Recursion Recursive set Relation (mathematics)Reverse mathematics Richard Dedekind Robinson arithmetic Rule of inference Russell's paradox Satisfiability Saturated model Schröder–Bernstein theorem Second-order arithmetic Second-order logic Self-verifying theories Semantic theory of truth Semantics of logic Sentence (mathematical logic)Sequent calculus Set-builder notation Set (mathematics)Set theory Signature (logic)Singleton (mathematics)Skolem arithmetic Soundness Spectrum of a sentence Spectrum of a theory Square of opposition Strength (mathematical logic)String (formal languages)Structure (mathematical logic)Subset Substitution (logic)Substructure (mathematics)Successor ordinal Supertask Surjective function Suslin's problem Syllogism Symbol (formal)Symmetric difference Syntax (logic)T-schema Tarski's axiomatization of the reals Tarski's axioms Tarski's theory of truth Tarski's undefinability theorem Tarski–Grothendieck set theory Tautology (logic)Term (logic)Term logic Theorem Theories of truth Theory (mathematical logic)Thomas Jech Thoralf Skolem Three-valued logic Timeline of mathematical logic Transfer principle Transfinite number Transfinite recursion theorem Transfinite sequence Transitive set True arithmetic Truth predicate Truth table Truth value Tuple Turing machine Type (model theory)Type theory Ultrafilter (set theory)Ultrafilter on a set Ultraproduct Uncountable set Undecidable problem Uninterpreted function Union (set theory)Uniqueness quantification Universal quantification Universal set Universe (mathematics)Urelement Vacuously true Validity (logic)Variable (mathematics)Vector space Venn diagram Vitali set Von Neumann universe Von Neumann–Bernays–Gödel set theory Well-formed formula Well-founded relation Well-order Well-ordering theorem Willard Van Orman Quine Zermelo set theory Zermelo–Fraenkel set theory Zorn's lemma

145 concepts already in your glossary