Anti-classification results for orbit equivalence relations

Specialeforsvar: Sofie Volder Jensen

Titel: Anti-classification results for orbit equivalence relations

Abstract: We introduce equivalence relations arising from topological groups acting on Polish spaces and Borel-reductions between equivalence problems. We prove two anti-classification results which are both due to Greg Hjorth [4]. In the first half we introduce cli-groups, and pinpoint a topological property, which obstructs the possibility of being cli-classifible. Then in the
second half we define turbulent group actions, and show that such are not classifiable to any countable structure. We will proof both results using the ideas presented by Lupini and Panagiotopoulos in [6] using infinite games.

Vejleder:  Asger D. Törnqvist
Censor:    Jesper Bengtson, IT Universitet