Kurt Gödel Research Center

2010 seminar talk: Solution to the pinned conjecture

Talk held by Jindrich Zapletal (University of Florida, Gainesville and Czech Academy of Sciences, Prague) at the KGRC seminar on 2010-12-09.

Abstract

The notion of a pinned equivalence relation is useful in proofs of irreducibility between Borel equivalence relations. Kechris conjectured that the smallest unpinned equivalence relation is equality of countable sets of reals. I will show that the answer is negative using old ideas of Shelah regarding Borel sets in the plane containing large squares. The talk will include the necessary background.