Friday, March 14, 20142:00 pmCUNY Logic WorkshopGC6417

# Structurability and countable Borel equivalence relations

## Robin Tucker-Drob

### Rutgers University

The dynamical and descriptive set theoretic complexity of a countable Borel equivalence relation E can often be understood in terms of the kinds of countable first order structures which are compatible with E in a suitable sense. In this talk I will make this suitable sense precise by discussing the notion of Borel structurability. I will also discuss some recent joint work with Brandon Seward in which we show that the equivalence relation generated by the free part of the translation action of a countable group G on its powerset is structurably-universal among equivalence relations generated by free Borel actions of G.