Definability of maximal cofinitary groups

Abstract

We present a proof of a result, previously announced by the second author, that there is a closed (even ${\Pi }_1^0$) set generating an $F_{\sigma }$ (even ${\Sigma }_2^0$) maximal cofinitary group (short, mcg) which is isomorphic to a free group. In this isomorphism class, this is the lowest possible definitional complexity of an mcg.

arXiv commentThis work is part of the first authors thesis