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Results tagged with continuum-hypothesis
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user 2000
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
Must uncountable standard models of ZFC satisfy CH?
Here is a dichotomy which is close to what you want.
Given a model $V$ of $\mathrm{ZFC} + \mathrm{CH}$.
If $\omega_1^V$ is inaccessible to reals then every real number is contained in an uncountable …
- 44.4k
18
votes
When $2^\alpha = 2^\beta$ implies $\alpha=\beta$ ($\alpha,\beta$ cardinals)
The Generalized Continuum Hypothesis, i.e. $2^\kappa = \kappa^+$ for every infinite cardinal $\kappa$, implies the desired result, but it can hold in other circumstances. For example, Woodin has shown …
- 44.4k