Caltech Logic Seminar, Pasadena, September 2021
Abstract: There are several well-studied “jumps” on the class of Borel equivalence relations under Borel reducibility, namely, the Friedman–Stanley jump and the family of Louveau jumps. In joint work with John Clemens, we defined a new (ish) family of jumps called Bernoulli jumps. In this talk I will introduce and describe Bernoulli jumps, and present an application to the classification of countable scattered orders. I will conclude by summarizing some recent developments (due to Shani and Allison) on Bernoulli jumps.