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A CO-ANALYTIC COHEN-INDESTRUCTIBLE MAXIMAL COFINITARY GROUP
Published online by Cambridge University Press: 19 June 2017
Abstract
Assuming 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.
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- Copyright © The Association for Symbolic Logic 2017
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