 Bukovský-Hechler theorem

If the power-set function is eventually constant below a singular cardinal $\kappa$, its constant value persists at $\kappa$. Writing $\theta =\mathrm{cf}(\kappa )$ gives $2^{\kappa }=(2^{<\kappa }{)}^{\theta }$. On the plateau choose a cardinal $\mu \ge \theta$, so $(2^{\mu }{)}^{\theta }=2^{\mu \cdot \theta }=2^{\mu }$.