A co-analytic Cohen indestructible maximal cofinitary group

Abstract

Assuming that every set is constructible, we find a ${\Pi }_1^1$ maximal cofinitary group of permutations of $\mathbb{N}$ which is indestructible by Cohen forcing. Thus we show that the existence of such groups is consistent with arbitrarily large continuum. Our method also gives a new proof, inspired by the forcing method, of Kastermans' result that there exists a ${\Pi }_1^1$ maximal cofinitary group in $L$.

Minor corrections

References in corpus (2)

• A Borel maximal cofinitary group
• On Horowitz and Shelah's Borel maximal eventually different family

Cited by in corpus (3)

• Constructing maximal cofinitary groups
• Tight Eventually Different Families
• Maximal discrete sets