# Asger Tornquist: An invariant set-theoretic approach to Mathias’ theorem

Place: Fields Institute (Room 210)

Date: May 20, 2016 (13:30-15:00)

Speaker: Asger Tornquist

Title: An invariant set-theoretic approach to Mathias’ theorem

Abstract: Mathias proved in 1969 that there are no infinite analytic
maximal almost disjoint families of subsets of $\omega$. His proof is
essentially Ramsey theoretical. A few years ago I found a “classical” proof
of this theorem which uses a tree/derivative argument. But in this talk, I
will give yet another proof, this time one that is closer in spirit to
Mathias’ original proof, but which avoids the Ramsey theoretical machinery
by instead using a bit of garden-variety invariant descriptive set theory.