Series: Penn State Logic Seminar Date: Wednesday, June 30, 2004 Time: 11:10 AM - 12:25 PM Place: 311 Boucke Building Speaker: John Clemens, Penn State, Mathematics Title: Turbulence, part 3 of 3 Abstract: A definable equivalence relation is said to be Classifiable by Countable Structures if there is a Borel way of assigning isomorphism types of countable structures as complete invariants. This is a useful benchmark for gauging the complexity of many equivalence relations. Hjorth's theory of Turbulence provides a powerful technique for showing that certain equivalence relations are not classifiable by countable structures. I will present the definition of a turbulent group action and the proof that such actions are not classifiable by countable structures. I will then discuss some applications of this theory to specific equivalence relations of interest.