Borel Conjecture for the Marczewski ideal

2024/01/09 by Brendle, Joerg, Wohofsky, Wolfgang
#03E05 #03E15 #03E17 #03E35 #03E50 #22A05 #54H11 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2401.04300

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.

Related

• Cofinalities of Marczewski-like ideals
• A lower density operator for the Borel algebra
• A Dedekind Finite Borel Set
• Borel's conjecture and meager-additive sets
• Weakly infinite dimensional subsets of R^N