= Singular cardinals hypothesis
{title2=$\gimel(\kappa)=\max\{\kappa^+,2^{\operatorname{cf}(\kappa)}\}$}
= SCH
{c}
{synonym}
The singular cardinals hypothesis asserts that every infinite <singular cardinal> $\kappa$ satisfies
$$
2^{\operatorname{cf}(\kappa)}<\kappa\ \Longrightarrow\ \gimel(\kappa)=\kappa^+.
$$
Equivalently, $\gimel(\kappa)=\max\{\kappa^+,2^{\operatorname{cf}(\kappa)}\}$ for every infinite <singular cardinal>. Here $\gimel$ is the <gimel function>. The <Generalized continuum hypothesis> implies this principle, but the principle only constrains the indicated singular-cardinal exponentiation.
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