generalized continuum hypothesis
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generalized continuum hypothesis
The generalized continuum hypothesis states that for any infinite cardinal there is no cardinal such that .
An equivalent condition is that for every ordinal . Another equivalent condition is that for every ordinal .
Like the continuum hypothesis, the generalized continuum hypothesis is known to be independent of the axioms of ZFC.
Keywords:
cardinality, cardinal
Synonym:
generalised continuum hypothesis, GCH
Type of Math Object:
Axiom
Major Section:
Reference
Groups audience:
Mathematics Subject Classification
03E50 no label found
