# 2009 seminar talk: Some reducibilities on k-partitions

Talk held by Victor Selivanov (Insitute of Informatics Systems, Siberian Division of Russian Academy of Science) at the KGRC seminar on 2009-10-06.

### Abstract

We discuss some extensions of the classical Wadge reducibility on Borel subsets of the Baire space. Main emphasis is made on the extension from the case of sets (i.e., 2-partitions) to the case of partitions of a space to k parts, for any k>1. We show, in particular, that for k>2 the structure of Wadge degreed becomes much more complicated (but still manageable) than for the case of sets. We also settle model-theoretic properties (like characterisation of the definable predicates) of some initial segments of the structures Wadge degrees.