Linked from

The 54 pages that link to Set theory, each with the reason it gives.

• John von NeumannNarrower topic: Von Neumann made major contributions to axiomatic set theory and its foundations.

• TopologyNarrower topic: Topological spaces are built on sets, with additional structure specifying open subsets.

• Bertrand RussellRelated: A contradiction in naive set theory prompted Russell’s best-known logical paradox.

• Georg CantorNarrower topic: Cantor established this field as a foundation for studying mathematical infinity.

• Type theoryCompared with: Set theory builds foundations from membership, whereas type theory organizes objects by types.

• Classical logicRelated: Classical logic is the standard underlying logic of much axiomatic set theory.

• Pigeonhole principleNarrower topic: The principle can be expressed as a theorem about functions between finite sets.

• Partial orderRelated: Partial orders provide structure for comparing sets and organizing set-theoretic arguments.

• Category theoryCompared with: Set theory organizes mathematics through membership, while category theory emphasizes maps and composition.

• Ordinal numberNarrower topic: Modern ordinal numbers are defined and studied within set theory.

• Proof theoryCompared with: It studies foundational objects and axioms rather than formal derivations themselves.

• CardinalityNarrower topic: Cardinality became a central measure within Cantor's developing theory of sets.

• Mathematical logicRelated: It became a dominant framework for expressing mathematical foundations, though it is not identical to logic.

• Richard DedekindRelated: His definition of infinite sets helped make set-theoretic reasoning part of mathematics.

• Andrey KolmogorovRelated: His probability axioms describe events as measurable sets.

• Formal systemRelated: Axiomatic set theories provide a prominent setting for formalizing mathematics.

• Cantor's theoremNarrower topic: Cantor’s theorem became a central result in the study of sets and infinity.

• Foundations of mathematicsRelated: It serves as a common framework for expressing much of modern mathematics.

• MathematicsRelated: It provides a common language for defining mathematical objects and structures.

• Second-order logicRelated: Second-order quantification can express set-theoretic principles in alternative foundations.

• Cantor's diagonal argumentNarrower topic: Cantor’s argument became a central proof technique in the development of this field.

• Axiom of extensionalityNarrower topic: The axiom is one of the foundational principles governing this subject.

• Axiom of pairingNarrower topic: Pairing is one of the basic existence principles in this framework.

• Bernard BolzanoNarrower topic: Bolzano’s writings anticipated questions later central to the formal study of sets.

• L. E. J. BrouwerCompared with: Brouwer challenged the classical foundations that treated mathematical entities as independently existing sets.

• Point (geometry)Narrower topic: Modern foundations commonly treat geometric spaces and their points as sets and elements.

• Wacław SierpińskiNarrower topic: Sierpiński helped develop set theory, including work on cardinal numbers and the axiom of choice.

• Foundations of GeometryRelated: Many formal treatments represent geometric points and structures using set-theoretic objects.

• Nicolas BourbakiNarrower topic: Bourbaki uses set-theoretic language as a broad foundation for its exposition.

• Philosophy of mathematicsBroader topic: Set theory provides a common framework for expressing much of modern mathematics.

• Axiom schema of specificationNarrower topic: Specification is a foundational principle governing set existence.

• Axiomatic systemNarrower topic: Set theory supplies a prominent foundational setting in which axiomatic systems are formulated.

• Felix HausdorffNarrower topic: Hausdorff used set-theoretic methods to formulate general spaces and investigate infinite collections.

• Ordinal analysisCompared with: Its large-cardinal hierarchies pose strength comparisons that ordinal analysis handles only in specialized forms.

• Pure mathematicsRelated: It provides a language for constructing and comparing mathematical objects.

• Higher-order logicRelated: Full higher-order semantics can be described using collections of sets and relations.

• Order theoryNarrower topic: Order relations are often defined as sets of ordered pairs.

• Richard RadoRelated: Set-theoretic methods underpin Rado’s results on infinite structures.

• ConstructivismNarrower topic: Constructivist mathematics can be developed by restricting how sets and their members are defined.

• Number (mathematics)Related: Set theory offers constructions of number systems and tools for comparing their sizes.

• Probability axiomsNarrower topic: Events and disjointness are expressed using set operations.

• Description logicRelated: Concepts are interpreted as sets of individuals, giving the language its standard semantics.

• Discrete mathematicsRelated: Sets provide a language for defining collections of discrete objects and their properties.

• Edgar F. CoddNarrower topic: Relations in Codd’s model are grounded in the mathematics of sets.

• Schröder–Bernstein theoremNarrower topic: The theorem arose from foundational questions about comparing infinite sets.

• Alain BadiouRelated: Badiou uses axiomatic set theory to describe being as pure multiplicity.

• Erdős–Rado theoremNarrower topic: The theorem's guarantees and bounds are formulated in set-theoretic language.

• Kőnig's lemmaRelated: The lemma's distinction between finite branching and infinite size is naturally expressed in set-theoretic terms.

• Venn diagramNarrower topic: Venn diagrams became visual tools for the language and operations of set theory.

• De Morgan's lawsNarrower topic: Set intersection, union, and relative complement realize the lattice identities.