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Results tagged with continuum-hypothesis
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user 30186
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.
5
votes
Accepted
Which extension of ZFC proves that ZFC can only prove CH satisfied by the first two sets?
The statement you propose is equivalent to consistency of GCH failing for all (infinite) cardinals. This problem is well-studied. Of course the theory ZFC+Con(ZFC+"GCH fails everywhere") gives an answ …
- 28.2k
29
votes
Accepted
On the probability of the truth of the continuum hypothesis
For any $E$ modelling ZFC and for each $n\in\omega$, we must have $(n,n)\not\in E$. Therefore $M_{ZFC}$ is contained in the cylinder set defined by $(0,0)\not\in E,\dots,(n,n)\not\in E$ which has meas …
- 28.2k