# Jumps in the Borel complexity hierarchy

Bristol Logic and Set Theory Seminar, November 2022

*Abstract*: There are several well-studied “jumps” on the class of Borel equivalence relations under Borel reducibility, which carry an equivalence relation to one of greater complexity. Examples include the jump of Friedman–Stanley and the jumps of Louveau. 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 more recent developments, due to others, relating to Bernoulli jumps.