Kurt Gödel Research Center

2008 seminar talk: Good Borel reducibilities for sets of reals

Talk held by Luca Motto Ros (KGRC) at the KGRC seminar on 2008-04-17.

Abstract

We will present an (almost) complete analysis (under AD) of Borel reducibilities using a quite general approach, and we will give various examples. In particular, we will show that the degree-structure induced by a good Borel reducibility is completely determined by its characteristic set (which correspond to the first nontrivial level of the corresponding hierarchy), and we will prove a dichotomy theorem for these structures. If time permits, we will also briefly describe the Martin-Monk method, which is one of the main tools involved in this theory.