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Results tagged with continuum-hypothesis
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user 109573
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.
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 …
- 4,316
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 …
- 4,316