J. D. Hamkins proved in "The foundation axiom and elementary self-embeddings of the universe" that, working in $ZFGC^− +BAFA$, there are nontrivial automorphisms and elementary embeddings of the universe V into itself.
But, he say "so (BAFA) there are no Reinhardt cardinals here to be found. The embeddings provided by BAFA have no critical points." in this post. What does he mean for "no critical points"?
(1) Can we use Kunen's inconsistency theorem to proof $ZFGC^- + BAFA + Reinhardt \to 0=1$?