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Questions about the continuum hypothesis, or where the continuum hypothesis or its negation plays a role. This tag is also suitable, by extension, to refer to the generalized continuum hypothesis and related issues.
24
votes
Accepted
Must uncountable standard models of ZFC satisfy CH?
Remarks (2) and (3) are added in this edit.
What Cohen's quoted proof outline is leaving implicit is the following statement in which $\mathrm{Con}(T)$ means "$T$ is consistent".
$(*)$ Assuming $\ …
5
votes
Are all models of ZF + DC + "All set of reals are lebesgue measurable" also models of CH?
The question seems to be an open research problem; it was posed in 2011 on MO (and has remained unanswered), see:
Lebesgue Measurability and Weak CH