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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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Accepted
Very Large Cardinal Axioms and Continuum Hypothesis
It is known in the folklore (I could never find a source for the results) that $I_0$, $I_1$, and $I_2$ cardinals are all indestructible by small forcing, meaning that we can force ${\rm CH}$ over a un …