Logic Seminar

We study the descriptive complexity of Borel binary relations, compared with the notion of continuous reducibility. In a first part, we present some important tools interesting for themselves. The second part is devoted to Borel equivalence relations. The last part, more recent, is about the generalization of some of the previous results to relations which are not necessarily equivalence relations. The case of graphs is particularily nice. Also, there is a surprising exception with the classes of rank two, related to topological Ramsey theory on the space of rational numbers.