= Solution
The <Generalized continuum hypothesis>[generalized continuum hypothesis] is
$$
\boxed{2^\kappa=\kappa^+\quad\text{for every infinite cardinal }\kappa.}
$$
Equivalently, for every <ordinal> $\alpha$, $2^{\aleph_\alpha}=\aleph_{\alpha+1}$. Here $2^\kappa$ is the <cardinality> of the <power set> of a <set> of <cardinality> $\kappa$, and $\kappa^+$ is the least strictly larger cardinal. The hypothesis says that no intermediate cardinal lies between an <infinite set> and its <power set>.
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