Borel conjecture for the Marczewski ideal

We show in ZFC that there is no set of reals of size continuum which can be translated away from every set in the Marczewski ideal. We also show that in the Cohen model, every set with this property is countable.

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Publication Details

Journal
Proceedings of the American Mathematical Society
Published
2024-10-02
DOI
https://doi.org/10.1090/proc/16981
Primary Topic
Advanced Topology and Set Theory
Type
article
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article

Borel conjecture for the Marczewski ideal

Jörg Brendle, Wolfgang Wohofsky
Proceedings of the American Mathematical Society
Advanced Topology and Set Theory
article

Borel conjecture for the Marczewski ideal

Jörg Brendle, Wolfgang Wohofsky
article en

Abstract

We show in ZFC that there is no set of reals of size continuum which can be translated away from every set in the Marczewski ideal. We also show that in the Cohen model, every set with this property is countable.

Proceedings of the American Mathematical SocietyVol. 152(12)
Universität Hamburg (DE), Kobe University (JP)
Openalex Percentile: Top 73%
Advanced Topology and Set Theory
DOISourceOpenAlex
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Borel conjecture for the Marczewski ideal — Jörg Brendle, Wolfgang Wohofsky · Proceedings of the American Mathematical Society (2024) | TGRS Research Map | TGRS