Hjorth's theory of turbulence
The purpose of this talk is to survey several results from Hjorth's theory of turbulent polish group actions.
We will start by discussing certain classification problems associated with Borel equivalence relations, and present the notions of Borel reductions and smooth relations, and the E_0 dichotomy theorem of Harrington-Kechris-Louveau.
We will then introduce the notions of logic space, classification by countable structures, and turbulent group actions. After discussing several basic results concerning turbulent actions, we will describe Hjorth's topological version of the classical Scott analysis, and sketch the proof of his theorem, showing that the orbit equivalence relation of any turbulent action cannot be classified by countable structures.
Wed, 05/12/2018 - 11:00 to 13:00