Alain Louveau

Although it has been known from the beginning of the theory that there are analytic equivalence relations which are complete, i. e maximum in the Borel reducibility ordering, no "concrete" such example was known -at least to my knowledge-, in particular no mathematical classification problem was known to be of that complexity. In this talk, I will give a few examples of such classification problems. This is a joint work with Christian Rosendal.The proofs are based on a dimension 2 representation result, analogous to the dimension 1 representation of analytic sets by non well founded trees.