Talk:Continuum hypothesis

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Doesn't Solovay's result require an upper bound on cardinality?

The section Independence from ZFC contains this sentence:

"A result of Solovay, proved shortly after Cohen's result on the independence of the continuum hypothesis, shows that in any model of ZFC, if $\kappa$ is a cardinal of uncountable cofinality, then there is a forcing extension in which $2^{\aleph _{0}}=\kappa$."

But the uncountable cofinality of such a 𝜅 must be ≤ $2^{\aleph _{0}}$, because otherwise 𝜅 > $2^{\aleph _{0}}$, and so 𝜅 ≠ $2^{\aleph _{0}}$.

If this is right, I hope that someone knowledgeable about this subject will fix this omission. — Preceding unsigned comment added by 98.36.148.11 (talk • contribs)

See Forcing (mathematics). "in any model of ZFC" refers to a situation where the model is a set, not the actual universe. So an "uncountable cardinal" Κ is only uncountable in the model, not in the actual universe. So you are mistaken. JRSpriggs (talk) 14:18, 23 November 2024 (UTC)