Greg Hjorth : Treeable equivalence relations

Posted by Matthias Aschenbrenner , part of the Logic Seminar.

At

Sept. 6, 2005, 4 p.m.

In

SEO 427

Abstract

An equivalence relation $E$ on $X$ is treeable if there is an acyclic graph $R$ which is Borel as a subset of $X\times X$ and whose connected components form the $E$-equivalence classes. I will survey what is known about treeable equivalence relations up to Borel reducibility and orbit equivalence. I will also mention a dichotomy theorem for when a treeable equivalence relation is reducible to one with countable classes and another dichotomy theorem for when it is possible to select an end from each equivalence class.