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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.

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Does small forcing preserve CH?

Yes. Let $X$ be a name for a subset of $\omega$. It can be described the following way: for every $i<\omega$ $\{p^i_\alpha:\alpha<\omega_1\}$ a maximal antichain, $\{\varepsilon^i_\alpha:\alpha<\omega …
Péter Komjáth's user avatar