Generalized Continuum Hypothesis

URI: https://gptkb.org/entity/Generalized_Continuum_Hypothesis
GPTKB entity
Statements (24)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:abbreviation gptkb:GCH
gptkbp:category gptkb:cardinal_arithmetic
open problem in mathematics
gptkbp:discusses gptkb:Principia_Mathematica
gptkb:Set_Theory_and_the_Continuum_Hypothesis_(Paul_Cohen)
gptkbp:field gptkb:set_theory
gptkbp:formedBy 1908
gptkbp:hasWikidataID gptkb:Q11277
https://www.w3.org/2000/01/rdf-schema#label Generalized Continuum Hypothesis
gptkbp:implies gptkb:Continuum_Hypothesis
gptkbp:independenceDate gptkb:Zermelo-Fraenkel_set_theory_with_the_Axiom_of_Choice_(ZFC)
gptkbp:influenced gptkb:forcing_(mathematics)
axiom of constructibility
gptkbp:proposedBy gptkb:Georg_Cantor
gptkbp:provenIndependentBy gptkb:Kurt_Gödel
gptkb:Paul_Cohen
gptkbp:provenIndependentIn 1940
1963
gptkbp:relatedTo gptkb:Continuum_Hypothesis
gptkbp:state For every infinite cardinal number \\( \\kappa \\), there is no cardinal number strictly between \\( \\kappa \\) and \\( 2^\\kappa \\).
gptkbp:bfsParent gptkb:constructible_universe
gptkb:Easton's_theorem
gptkbp:bfsLayer 6