The words set theory can be used to mean a number of subtly different things in mathematics:

• Naive set theory is the original set theory developed by mathematicians at the end of the 19th century.
• Axiomatic set theory is a rigorous axiomatic theory developed in response to the discovery of serious flaws (such as Russell's Paradox) in naive set theory.
• Internal set theory is an axiomatic extension of set theory that supports a logically consistent identification of illimited (enormously large) and infinitesimal elements within the Real numbers.
• Various versions of logic have associated sorts of sets (such as fuzzy sets in fuzzy logic).

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C

• Cardinal numbers

Articles in category "Set theory"

There are 192 articles in this category.

Set theory A Aleph number Almost Almost Ramsey cardinal Alternative set theory Analytical hierarchy Antisymmetric relation Arithmetical hierarchy Axiom of choice Axiom of constructibility Axiom of countable choice Axiom of dependent choice Axiom of determinacy Axiom of empty set Axiom of extensionality Axiom of infinity Axiom of pairing Axiom of power set Axiom of projective determinacy Axiom of real determinacy Axiom of regularity Axiom of union Axiom schema of replacement Axiom schema of specification Axiomatic set theory Axiomatizable class B Banach-Mazur game Beth number Beth two Bijection Binary relation Blardy Brazilian logic Burali-Forti paradox C Cantor set Cantor's diagonal argument Cantor's first uncountability proof Cantor's theorem Cantor-Bernstein-Schroeder theorem Cardinal assignment Cardinal number Cardinality Cardinality of the continuum Cartesian product Choice function Class (set theory) Club filter Club set Clubsuit Cocountable Codomain Cofinal (mathematics) Cofinality Cofinite Complement (set theory) Constructible universe Continuum hypothesis Countable set Covering lemma Cyclic order D Dedekind infinite Definable number Descriptive set theory Diagonal intersection

D cont. Diamondsuit Disjoint union Domain (mathematics) E Element (mathematics) Empty function Empty set Equaliser Equinumerosity Equivalence class Equivalence relation Even and odd functions F Fixed-point lemma for normal functions Fodor's lemma Forcing (mathematics) Freiling's axiom of symmetry Function (mathematics) Fuzzy set Fuzzy set operations G Galileo's paradox Gimel function Goodstein's theorem Grothendieck universe H Hausdorff maximality theorem Hereditarily finite set Hilbert's paradox of the Grand Hotel Horizontal line test Huge cardinal Hyper-Woodin cardinal I Image (mathematics) Inaccessible cardinal Inclusion (mathematics) Indicator function Ineffable cardinal Injective function Inner model Integer Interesting number paradox Internal set theory Intersection (set theory) Inverse function K Kripke-Platek set theory Kripke-Platek set theory with urelements König's theorem L Large cardinal Limit cardinal Limit ordinal List of statements undecidable in ZFC M Mahlo cardinal Map (mathematics) Mostowski collapse Multiset Multivalued function N Naimark's problem Naive set theory Natural number New Foundations Non-empty set Non-well-founded set theory Normal function O On Numbers and Games Ordered pair Ordered partition of a set Ordinal number P PCF theory Pairing function

P cont. Partial function Partially ordered set Partition of a set Positive set theory Power set Primitive notion Property B Prototile R Range (mathematics) Rank (set theory) Rank-into-rank Record linkage Reflexive relation Regular cardinal Relation (mathematics) Remarkable cardinal Rough set Russell's paradox S Semiset Set Set of all sets Set-builder notation Set-theoretic definition of natural numbers Set-theoretic limit Singleton (mathematics) Stationary set Stratification (mathematics) Strongly inaccessible cardinal Subset Subtle cardinal Successor cardinal Successor ordinal Superhuge cardinal Surjection Suslin's problem Symmetric difference Symmetric relation T The algebra of sets Total order Transfinite induction Transfinite number Transitive closure Transitive relation Transversal Tychonoff's theorem U Ultrafilter lemma Uncountable set Union (set theory) Universe (mathematics) Ur-element V Venn diagram Von Neumann cardinal assignment Von Neumann universe Von Neumann-Bernays-Gödel set theory W Weakly compact cardinal Well-founded relation Well-ordering principle Well-ordering theorem Whitehead problem Z Zermelo set theory Zermelo-Fraenkel set theory Zero sharp Zorn's lemma