# Bernoulli jumps of equivalence relations

University of Florida Logic Seminar, Gainesville, November 2020

*Abstract*: There are several well-studied “jump operators” on the class of Borel equivalence relations under Borel reducibility, such as the Friedman–Stanley jump and the Louveau jumps. I will define and discuss the new (ish) Bernoulli jumps; for each countable group Gamma there is a Gamma-jump operator. I will discuss which groups give rise to proper jumps (E is strictly below the Gamma-jump of E). Finally I will present applications to the classification of countable scattered orderings, and to finding new benchmarks in the Borel complexity hierarchy. This is joint work with John Clemens.