# 2005 seminar talk: Critical Points of Rank-to-Rank Embeddings

Talk held by Andrew Brooke-Taylor (MIT) at the KGRC seminar on 2005-04-19.

### Abstract

One of the strongest large cardinal axioms we have posits the existence of an elementary embedding j from V_\lambda to V_\lambda for some limit ordinal \lambda. A peculiarity of it is that one such j will generate infinitely many more, not only through composition but also through the process of applying oneembedding to the graph of another.
I will talk about the structure generated in this way, and in particular the critical points of these embeddings.