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.

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All labels observed (4)

Label	Occurrences
set theory canonical	6
Cantorian set theory	1
Mengenlehre	1
set theory with urelements	1

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 ⓘ surface form: 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 ⓘ surface form: Russell's paradox axiom of choice ⓘ surface form: 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 (9)

Full triples — surface form annotated when it differs from this entity's canonical label.

Stanislaw Ulam → fieldOfWork → set theory ⓘ

axiom of choice → field → set theory ⓘ

Abraham Fraenkel → fieldOfWork → set theory ⓘ

Kronecker’s finitism → opposes → set theory ⓘ

this entity surface form: Cantorian set theory

Felix Hausdorff → notableWork → set theory ⓘ

this entity surface form: Mengenlehre

Thoralf Skolem → influenced → set theory ⓘ

New Foundations for Mathematical Logic → field → set theory ⓘ

Fraenkel–Mostowski permutation models → relatedToTheory → set theory ⓘ

this entity surface form: set theory with urelements

JAMS → subjectArea → set theory ⓘ