# Asger Törnquist: Analytic eventually different families of functions are not maximal

28/June/2013, 13:30-15:00
Fields Institute, Room 210

Speaker: Asger Törnquist

Title: Analytic eventually different families of functions are not maximal

Abstract: A well-known result of Mathias says that an infinite maximal almost disjoint family of subsets of $\omega$ is never analytic. The question has been raised if a maximal family of eventually different functions on $\omega$ can be analytic. In this talk, I will present a proof that it can’t be. We also obtain a new (and quite different) proof of Mathias’ theorem. Towards the end of the talk, I will discuss how the proofs can be adapted to show that maximal cofinitary families and groups of permutations of $\omega$ can’t be analytic either.