On the consistency of ZF with an elementary embedding from Vλ+2 into Vλ+2

Abstract

According to a theorem due to Kenneth Kunen, under ZFC, there is no ordinal λ and nontrivial elementary embedding j: Vλ+2→Vλ+2. His proof relied on the Axiom of Choice (AC), and no proof from ZF alone is has been discovered. I0,λ is the assertion, introduced by Hugh Woodin, that λ is an ordinal and there is an elementary embedding j: L(Vλ+1)→L(Vλ+1) with critical point