Algebra Seminar talk
2026-06-26
Max Scheiderbauer
Periodicity in the cumulative hierarchy
Abstract:
Kunen showed that $\mathrm{ZFC}(j)$, where $j: V\rightarrow V$ is a nontrivial elementary embedding, is inconsistent. We begin with a brief introduction to the large cardinal principles near the consistency strength of such embeddings in the context of ZF. We then present a theorem of Goldberg and Schlutzenberg on the definability of rank-into-rank embeddings, followed by results on the existence and structure of such embeddings.