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).
Subcategories
This category has the following 18 subcategories, out of 18 total.
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Pages in category "Set theory"
The following 142 pages are in this category, out of 142 total. This list may not reflect recent changes (learn more).
B
C
- Cabal (set theory)
- Cantor's diagonal argument
- Cantor's first set theory article
- Cantor's paradise
- Cantor's theorem
- Cardinal assignment
- Cardinality of the continuum
- Categorical set theory
- Chang's conjecture
- Class (set theory)
- Class logic
- Club filter
- Club set
- Clubsuit
- Code (set theory)
- Cofinality
- Condensation lemma
- Conglomerate (set theory)
- Continuous function (set theory)
- Continuum (set theory)
- Controversy over Cantor's theory
- Cumulative hierarchy
- Cylinder (algebra)
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H
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S
- S (set theory)
- Schröder–Bernstein property
- Scott's trick
- Separating set
- Set intersection oracle
- Set notation
- Set theory of the real line
- Set Theory: An Introduction to Independence Proofs
- Set-builder notation
- Set-theoretic limit
- Set-theoretic topology
- Sierpiński set
- Soft set
- Solovay model
- Square principle
- Stationary set
- Stratification (mathematics)
- Structuralism (philosophy of mathematics)
- Subclass (set theory)
- Successor cardinal
- Sunflower (mathematics)
- Superstrong cardinal
- Supertransitive class
- Support (mathematics)
- Suslin representation
- Symmetric set
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