# 2018 seminar talk: On the Complexity of Maximal Cofinitary Groups

Talk held by David Schrittesser (KGRC) at the KGRC seminar on 2018-01-11.

### Abstract

A maximal cofinitary group is a subgroup of the group of permutations of the set of natural numbers $\mathbb{N}$ such that any group element has only finitely many fixed points, and no strictly larger group of permutations of $\mathbb{N}$ has this property. Improving a result of Horowitz and Shelah, we show that there is a closed maximal cofinitary group.