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Questions about the generalized continuum hypothesis.

Questions about the generalized continuum hypothesis (GCH).

Generalized continuum hypothesis says that $\aleph_{\alpha+1}=2^{\aleph_\alpha}$ for every ordinal $\alpha$. GCH significantly simplifies cardinal exponentiation.

GCH is known to be independent of ZFC. (Both GCH and its negation are relatively consistent.)