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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 $\ …
Ali Enayat's user avatar
  • 17.7k
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
Ali Enayat's user avatar
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