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Results tagged with continuum-hypothesis
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user 15570
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.
17
votes
2
answers
1k
views
Is it consistent with ZFC that the real line is approachable by sets with no accumulation po...
Let $P$ denote the following proposition:
There exists a set $S$ of subsets of $\mathbb{R}$ such that
$S$ is totally ordered by inclusion;
each member of $S$ has no accumulation points;
the union of …
- 708
8
votes
3
answers
690
views
Is "the purely probabilistic version of Freiling's axiom of symmetry" disprovable in ZFC?
I'm trying to pinpoint the "intuitive argument" for Freiling's Axiom of Symmetry. It's meant to be a "probabilistic" argument, so thinking about what seems to me to be the probabilistic intuition, it …
- 708
47
votes
10
answers
5k
views
What is the most "concrete-feeling" equivalent formulation of the Continuum Hypothesis that ...
There are many equivalent formulations of the Continuum Hypothesis, but I think the most standard one is that
there is no infinite cardinality lying strictly between the cardinality of the natural nu …