On the Algebra of Elementary Embeddings of a Rank into Inself

Abstract

Let $j:V_λ---> V_λ$ be an elementary embedding, with critical point $κ$, and let $f(n)$ be the number of critical points of embeddings in the algebra generated by $j$ which lie between $j^n(κ)$ and $j^{n+1}(κ)$. It is shown that $f(n)$ is finite for all $n$.