A CO-ANALYTIC COHEN-INDESTRUCTIBLE MAXIMAL COFINITARY GROUP

Abstract

AbstractAssuming that every set is constructible, we find a ${\text{\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 ${\text{\Pi }}_1^1 $ maximal cofinitary group in L.