Generalized Continuum Hypothesis (GCH)
GPTKB entity
Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:canBeAssumedConsistentlyWith |
gptkb:ZFC
|
| gptkbp:canBeNegatedConsistentlyWith |
gptkb:ZFC
|
| gptkbp:concerns |
infinite sets
power set cardinal numbers |
| gptkbp:doesNotFollowFrom |
gptkb:Zermelo-Fraenkel_set_theory_with_Choice_(ZFC)
|
| gptkbp:field |
gptkb:set_theory
|
| gptkbp:firstPublished |
1900
|
| gptkbp:formedBy |
gptkb:Georg_Cantor
|
| https://www.w3.org/2000/01/rdf-schema#label |
Generalized Continuum Hypothesis (GCH)
|
| gptkbp:implies |
gptkb:Continuum_Hypothesis
|
| gptkbp:independenceProvedBy |
gptkb:Kurt_Gödel
gptkb:Paul_Cohen |
| gptkbp:listedOn |
gptkb:Hilbert's_problems
gptkb:Hilbert's_first_problem |
| gptkbp:relatedTo |
gptkb:Continuum_Hypothesis
|
| gptkbp:state |
For every infinite cardinal number κ, there is no cardinal number strictly between κ and 2^κ
|
| gptkbp:status |
independent of ZFC
|
| gptkbp:symbol |
gptkb:GCH
|
| gptkbp:bfsParent |
gptkb:constructible_universe_(L)
|
| gptkbp:bfsLayer |
7
|