set theory | DisamKB

set theory

E85409

branch of mathematical logic branch of mathematics

Set theory is a foundational branch of mathematical logic that studies collections of objects, called sets, and underpins much of modern mathematics.

Statements (57)

Predicate	Object
instanceOf	branch of mathematical logic → branch of mathematics →
centralQuestion	comparisons of infinite cardinalities → nature of infinity →
developedBy	Georg Cantor →
fieldOfStudy	foundations of mathematics → sets →
hasAxiomSystem	Kripke–Platek set theory → Zermelo–Fraenkel set theory → Zermelo–Fraenkel set theory with Choice → naive set theory → von Neumann–Bernays–Gödel set theory →
hasFoundationIn	axiomatic systems →
hasSubfield	combinatorial set theory → descriptive set theory → determinacy theory → inner model theory → set-theoretic topology →
historicalPeriod	late 19th century →
includesConcept	Aleph numbers → Russell's paradox → Zorn's lemma → axiom of choice → cardinal arithmetic → constructible universe → continuum hypothesis → empty set → forcing → large cardinals → ordinal arithmetic → universal set → well-ordering theorem →
isFoundationFor	abstract algebra → analysis → category theory → functional analysis → measure theory → most of modern mathematics → topology →
languageUsed	first-order logic →
studies	cardinal numbers → cardinality → collections of objects → functions → infinite sets → intersections → membership relations → ordinal numbers → power sets → relations → subsets → unions →
usesConcept	intersection symbol ∩ → membership symbol ∈ → power set operator P(X) → subset symbol ⊆ → union symbol ∪ →

Referenced by (3)

Subject (surface form when different)	Predicate
Abraham Fraenkel → Stanislaw Ulam →	fieldOfWork
axiom of choice →	field