The foundation axiom and elementary self-embeddings of the universe

Abstract

We consider the role of the foundation axiom and various anti-foundation axioms in connection with the nature and existence of elementary self-embeddings of the set-theoretic universe.

arXiv comment25 pages. Discussion and commentary concerning this article can be made at http://jdh.hamkins.org/the-role-of-foundation-in-the-kunen-inconsistency/. Version 2 has minor changes and a change in title