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Set Theory Seminar: Shaun Allison (HUJI) | Einstein Institute of Mathematics

Set Theory Seminar: Shaun Allison (HUJI)

Date: 
Wed, 22/12/202114:00-16:00

Title: 
Applications of the Hjorth analysis of Polish group actions


Abstract:
After reviewing the Scott analysis of countable structures, which can be viewed as the analysis of continuous actions of S_\infty on Polish spaces, we describe a generalization proposed by Hjorth to actions of arbitrary Polish groups. Time permitting, two major applications will be discussed. The first is a technique to detect when an equivalence relation cannot be classifiable by abelian Polish groups or more generally Polish groups with a two-sided invariant metric (TSI), which is joint work with Aristotelis Panagiotopoulos. The second is the construction of actions of abelian Polish groups of high (Borel) complexity, which contains joint work with Assaf Shani.