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A CO-ANALYTIC COHEN-INDESTRUCTIBLE MAXIMAL COFINITARY GROUP

Published online by Cambridge University Press:  19 June 2017

VERA FISCHER ,
DAVID SCHRITTESSER  and
ASGER TÖRNQUIST
VERA FISCHER
Affiliation:
KURT GÖDEL RESEARCH CENTER UNIVERSITÄT WIEN, WÄHRINGERSTRAßE 25 1080 WIEN AUSTRIAE-mail: vera.fischer@univie.ac.at
DAVID SCHRITTESSER
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCES UNIVERSITY OF COPENHAGEN UNIVERSITETSPARKEN 5 2100 COPENHAGEN DENMARKE-mail:david.s@math.ku.dk
ASGER TÖRNQUIST
Affiliation:
DEPARTMENT OF MATHEMATICAL SCIENCES UNIVERSITY OF COPENHAGEN UNIVERSITETSPARKEN 5 2100 COPENHAGEN DENMARKE-mail: asgert@math.ku.dk
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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.

Keywords

03E1503E35descriptive set theoryconsistency and independence resultsmaximal cofinitary groupsconstructible setsCohen forcingco-analytic
Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 2 , June 2017 , pp. 629 - 647
Copyright
Copyright © The Association for Symbolic Logic 2017 

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