For sets $x, y$, let $x\approx y$ mean that there is a bijection $\varphi:x\to y$. The Weak Power Hypothesis (WPH) states that
if $x,y$ are sets and ${\cal P}(x)\approx {\cal P}(y)$ then $x\approx y$.
It appears to be open whether (WPH) implies the Axiom of Choice or even the Partition Principle.
Question. Is there a model of ${\sf ZFC}$ where (WPH) holds, but not (CH)?
