On a cofinal Reinhardt embedding without Powerset

Abstract

In this paper, we provide a positive answer to the question of Matthews whether ${\mathsf{ZF}}^{-}$ is consistent with a non-trivial cofinal Reinhardt elementary embedding $j:V\to V$. The consistency follows from $\mathsf{ZFC}+I_0$, and more precisely, it is witnessed by Schlutzenberg's model of $\mathsf{ZF}$ with an elementary embedding $k:V_{\hat{I}»+2}\to V_{\hat{I}»+2}$.

16 pages, final version