= Gimel hypothesis
{title2=$\gimel(\kappa)=\max\{\kappa^+,2^{\operatorname{cf}(\kappa)}\}$}
For every singular infinite <cardinal number> $\kappa$, the <Gimel function> has the smallest value permitted by <König theorem for cardinal numbers> and the exponent: $\kappa^{\operatorname{cf}(\kappa)}=\max\{\kappa^+,2^{\operatorname{cf}(\kappa)}\}$. Where $2^{\operatorname{cf}(\kappa)}<\kappa$, this is the <singular cardinals hypothesis>. The hypothesis imposes no separate successor-power condition on regular <cardinals>.
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