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Results tagged with continuum-hypothesis
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user 57114
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.
9
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Accepted
Is it known whether or not $\aleph_\alpha=\beth_\alpha$ can be proven by ZFC?
Claim. For any $\alpha >0 \colon$ $\mathrm{ZFC} \not \vdash \mathrm{CH}(\aleph_{\alpha})$
Proof. Starting with $L$, we may enlarge the continuum $\beth_1$ arbitrarily without changing cardinals. In p …
- 1,080
10
votes
Does $V = \textit{Ultimate }L$ imply GCH?
During this year's conferene on inner model theory in Münster, Gabriel Goldberg proved that the so-called Ultrapower Axiom implies that $\mathrm{GCH}$ holds above a supercompact cardinal (and since th …
- 1,080