Bukovský-Hechler theorem
= Bukovský-Hechler theorem
{c}
{title2=$2^\kappa=\lim_{\mu<\kappa}2^\mu\text{ on an eventual plateau}$}
If the power-set <function> is eventually constant below a <singular cardinal> $\kappa$, its constant value persists at $\kappa$. Writing $\theta=\operatorname{cf}(\kappa)$ gives $2^\kappa=(2^{<\kappa})^\theta$. On the plateau choose a <cardinal> $\mu\ge\theta$, so $(2^\mu)^\theta=2^{\mu\cdot\theta}=2^\mu$.