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3 results

5 - Some consistency results in ZFC using AD
from Part VII - Extensions of AD, Models with Choice
- By W. Hugh Woodin
Edited by Alexander S. Kechris, California Institute of Technology, Benedikt Löwe, Universiteit van Amsterdam, John R. Steel, University of California, Berkeley
Book:

Large Cardinals, Determinacy and Other Topics

Published online:

27 October 2020

Print publication:

05 November 2020, pp 104-129
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11 - More saturated ideals
from Part VIII - Other Topics
- By Matthew Foreman
Edited by Alexander S. Kechris, California Institute of Technology, Benedikt Löwe, Universiteit van Amsterdam, John R. Steel, University of California, Berkeley
Book:

Large Cardinals, Determinacy and Other Topics

Published online:

27 October 2020

Print publication:

05 November 2020, pp 223-247
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A CO-ANALYTIC COHEN-INDESTRUCTIBLE MAXIMAL COFINITARY GROUP
VERA FISCHER, DAVID SCHRITTESSER, ASGER TÖRNQUIST
Journal:

The Journal of Symbolic Logic / Volume 82 / Issue 2 / June 2017

Published online by Cambridge University Press:

19 June 2017, pp. 629-647

Print publication:

June 2017
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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.