Category:Set theory
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Set theory is any of 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, treating sets simply as collections of things.
- 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. It treats sets as "whatever satisfies the axioms", and the notion of collections of things serves only as motivation for the axioms.
- 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).
Pages in category "Set theory"
The following 200 pages are in this category, out of 248 total.
(previous page) (next page)A
- AD plus
- Aleph number
- Algebra of sets
- Almost
- 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
C
- Cantor set
- Cantor's diagonal argument
- CantorBernsteinSchroeder theorem
- Cantors diagonal argument
- Cantors first uncountability proof
- Cantors paradox
- Cantors theorem
- Cardinal assignment
- Cardinal number
- Cardinality
- Cardinality of the continuum
- Cartesian product
- CategoryDeterminacy
- CategoryOrdinal numbers
- Choice function
- Class (set theory)
- Class set theory
- Club filter
- Club set
- Clubsuit
- Cocountable
- Codomain
- Cofinal mathematics
- Cofinality
- Cofinite
- Complement (set theory)
- Complement set theory
- Complete Boolean algebra
- Constructible universe
- Continuum hypothesis
- Controversy over Cantors Theory
- Countable
- Countable set
- Covering lemma
- Cyclic order