Sheila Miller: Critical sequences of rank-to-rank embeddings and a tower of finite left distributive algebras

Time: Friday 10 October, 13:30-15:00

Place: Fields Institute, Room 210

Speaker: Sheila Miller

Title: Critical sequences of rank-to-rank embeddings and a tower of finite left distributive algebras

Abstract: In the early 1990’s Richard Laver discovered a deep and striking correspondence between critical sequences of rank-to-rank embeddings and finite left distributive algebras on integers. Each $A_n$ in the tower of finite algebras can be defined purely algebraically, with no reference to the elementary embeddings, and yet there are facts about the Laver tables that have only been proven from a large cardinal assumption. We present here some of Laver’s foundational work on the algebra of critical sequences of rank-to-rank embeddings and some work of the author’s, describe how the finite algebras arise from the large cardinal embeddings, and mention several related open problems.