Logic Seminar

I will present a dichotomy for equivalence relations on Polish spaces that can be expressed as countable unions of smooth Borel subequivalence relations. It can be seen as an extension of Kechris-Louveau's dichotomy for hypersmooth Borel equivalence relations. A generalization of our dichotomy, for equivalence relations that can be expressed as countable unions of Borel equivalence relations belonging to certain fixed classes, will also be presented. This is a joint work with Benjamin Miller.