A co-analytic cohen-indestructible maximal cofinitary group

Vera Fischer; David Schrittesser; Asger Törnquist

doi:10.1017/jsl.2017.5

A co-analytic cohen-indestructible maximal cofinitary group

Vera Fischer
, David Schrittesser
, Asger Törnquist

Universita Twien
University of Copenhagen

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Assuming that every set is constructible, we find a ∏₁¹ maximal cofinitary group of permutations of 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 ∏₁¹ maximal cofinitary group in L.

Original language	English
Pages (from-to)	629-647
Number of pages	19
Journal	Journal of Symbolic Logic
Volume	82
Issue number	2
DOIs	https://doi.org/10.1017/jsl.2017.5
State	Published - 1 Jun 2017
Externally published	Yes

Keywords

Co-analytic
Cohen forcing
Consistency and independence results
Constructible sets
Descriptive set theory
Maximal cofinitary groups

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10.1017/jsl.2017.5

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abstract = "Assuming that every set is constructible, we find a ∏11 maximal cofinitary group of permutations of 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 ∏11 maximal cofinitary group in L.",

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author = "Vera Fischer and David Schrittesser and Asger T{\"o}rnquist",

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N2 - Assuming that every set is constructible, we find a ∏11 maximal cofinitary group of permutations of 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 ∏11 maximal cofinitary group in L.

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KW - Co-analytic

KW - Cohen forcing

KW - Consistency and independence results

KW - Constructible sets

KW - Descriptive set theory

KW - Maximal cofinitary groups

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A co-analytic cohen-indestructible maximal cofinitary group

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Keywords

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