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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.
13
votes
Is it consistent with ZFC that the real line is approachable by sets with no accumulation po...
Here's a ZF proof that if $S$ is a chain of sets with $\bigcup S = \mathbb{R},$ then there is $X \in S$ which contains a countable set dense in some nonempty open set.
If there is $X \in S$ such that …
3
votes
Is "the purely probabilistic version of Freiling's axiom of symmetry" disprovable in ZFC?
In any model of ZFC where there is no such set for $c=1$ (e.g., Friedman's model mentioned in Gro-Tsen's answer), there is no $S \subset [0,1]^2$ such that all vertical slices $S_x$ are null and all h …