Gödel 1940 monograph "The Consistency of the Continuum Hypothesis"

E446860

mathematical monograph work in set theory

Gödel's 1940 monograph "The Consistency of the Continuum Hypothesis" is a landmark work in set theory that introduced the constructible universe (L) and proved that the Continuum Hypothesis and the Axiom of Choice are consistent with Zermelo–Fraenkel set theory, assuming ZF itself is consistent.

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All labels observed (1)

Label	Occurrences
Gödel 1940 monograph "The Consistency of the Continuum Hypothesis" canonical	1

Statements (44)

Predicate	Object
instanceOf	mathematical monograph ⓘ work in set theory ⓘ
assumption	consistency of Zermelo–Fraenkel set theory ⓘ
author	Kurt Gödel NERFINISHED ⓘ
defines	L as union of Lα over all ordinals α ⓘ Lα for each ordinal α ⓘ constructible hierarchy ⓘ
field	mathematical logic ⓘ set theory ⓘ
hasAbbreviation	Consistency of CH NERFINISHED ⓘ Gödel 1940 NERFINISHED ⓘ
hasImpactOn	debates on Platonism and constructivism in set theory ⓘ philosophy of mathematics ⓘ
historicalSignificance	first major consistency proof in axiomatic set theory beyond ZF ⓘ introduced the constructible universe as a central object in set theory ⓘ showed independence of CH and AC could not be refuted from ZF alone assuming ZF consistency ⓘ
influenced	development of inner model theory ⓘ subsequent independence results in set theory ⓘ
introducesConcept	constructible universe L ⓘ
language	English ⓘ
mainTopic	Axiom of Choice NERFINISHED ⓘ Continuum Hypothesis NERFINISHED ⓘ constructible universe ⓘ
placeOfPublication	Princeton NERFINISHED ⓘ
provesProperty	L is a transitive class ⓘ L satisfies all axioms of Zermelo–Fraenkel set theory ⓘ L satisfies the Axiom of Choice ⓘ L satisfies the Generalized Continuum Hypothesis ⓘ every set in L is constructible from earlier stages of the hierarchy ⓘ
provesResult	relative consistency of the Axiom of Choice with Zermelo–Fraenkel set theory ⓘ relative consistency of the Continuum Hypothesis with Zermelo–Fraenkel set theory ⓘ
publicationYear	1940 ⓘ
publisher	Princeton University Press NERFINISHED ⓘ
relatedWork	Cohen’s 1963 forcing proof of the independence of the Continuum Hypothesis ⓘ Gödel’s incompleteness theorems NERFINISHED ⓘ
series	Annals of Mathematics Studies NERFINISHED ⓘ
shows	if ZF is consistent then ZF+AC is consistent ⓘ if ZF is consistent then ZF+AC+CH is consistent ⓘ if ZF is consistent then ZF+CH is consistent ⓘ
subjectOf	expository articles on the constructible universe ⓘ historical studies in the foundations of mathematics ⓘ
title	The Consistency of the Continuum Hypothesis NERFINISHED ⓘ
usesMethod	definability hierarchy over ordinals ⓘ inner model L ⓘ

Referenced by (1)

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

constructible universe → hasReferenceWork → Gödel 1940 monograph "The Consistency of the Continuum Hypothesis" ⓘ