Work in $\sf ZFCA$ and permutation models has preceded forcing by several decades. Was it used to settle the question of the Generalized Continuum Hypothesis $\sf GCH$ when urelements are admitted? I mean we can have models of $\sf ZFCA$ in which there exist sets that are not comparable to any pure set, and so $\sf GCH$ is no longer a problem of the pure set world in that setting. So, we can formalize $\sf GCH$ as: given any infinite set $A$, there doesn't exist any set $B$ that is strictly supernumerous to $A$ and strictly subnumerous to $\mathcal P(A)$. Where strict super- and sub-numerous are defined in the usual manner after existence injections and non-existence of a bijection. My naive expectation is that permutation models are to settle such issue? Can they? Or otherwise, is there a version of forcing that works with urelements?