Consistency of Reinhardt Cardinals without Choice
Determine whether ZFR is consistent, where ZFR is the first-order theory ZF(j) plus the assertion that a nontrivial function symbol j:V->V is Sigma_1-elementary and hence fully elementary as a theorem scheme.
Source: F. Schlutzenberg, Reinhardt cardinals and iterates of V, Ann. Pure Appl. Logic 173 (2022)..
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