Math 2.0

Mathematical logic and foundations Set theory: axioms and basics Concept

Set theory

Builds on SetElementZermelo–Fraenkel set theory

Summary

Set theory is the branch of mathematical logic that studies sets, collections of objects called their elements. Cantor created it in the 1870s, with his study of infinite sets and their sizes. In its axiomatic form, most often Zermelo–Fraenkel set theory with choice, it serves as the standard foundation of mathematics. Its own subjects include ordinals and cardinals, independence results, large cardinals and descriptive set theory.

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Element, definition, no evidence levelElementdefinitionProposition, concept, no evidence levelPropositionconceptSet, concept, no evidence levelSetconceptSet, definition, no evidence levelSetdefinitionConjunction, definition, no evidence levelConjunctiondefinitionDisjunction, definition, no evidence levelDisjunctiondefinitionImplication, definition, no evidence levelImplicationdefinitionNegation, definition, no evidence levelNegationdefinitionPredicate, definition, no evidence levelPredicatedefinitionBiconditional, definition, no evidence levelBiconditionaldefinitionUniversal quantifier, definition, no evidence levelUniversal quantifierdefinitionAxiom of extensionality, statement, no evidence levelAxiom of extensionali…statementPropositional logic, concept, no evidence levelPropositional logicconceptPredicate logic, concept, no evidence levelPredicate logicconceptZermelo–Fraenkel set theory, concept, no evidence levelZermelo–Fraenkel set …conceptSet theory, concept, no evidence levelSet theoryconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Element definition
  2. Proposition concept
  3. Set concept
  4. Set definition
  5. Conjunction definition
  6. Disjunction definition
  7. Implication definition
  8. Negation definition
  9. Predicate definition
  10. Biconditional definition
  11. Universal quantifier definition
  12. Axiom of extensionality statement
  13. Propositional logic concept
  14. Predicate logic concept
  15. Zermelo–Fraenkel set theory concept
  16. Set theory concept

Where this leads

2 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Set_theory
About this page
TagRTHHCX84HN
URIm2://RTHHCX84HN
Kindconcept
WritingW0 stub
MSC03E30, 03E99
UsesSet, Element, Zermelo–Fraenkel set theory
Same as
Changed2 November 2026

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