English

Borel's conjecture and meager-additive sets

Logic 2021-04-08 v2 General Topology

Abstract

We prove that it is relatively consistent with ZFC\mathrm{ZFC} that every strong measure zero subset of the real line is meager-additive while there are uncountable strong measure zero sets (i.e., Borel's conjecture fails). This answers a long-standing question due to Bartoszy\'nski and Judah.

Cite

@article{arxiv.2012.02396,
  title  = {Borel's conjecture and meager-additive sets},
  author = {Daniel Calderón},
  journal= {arXiv preprint arXiv:2012.02396},
  year   = {2021}
}

Comments

12 pages, accepted in Proc. Amer. Math. Soc

R2 v1 2026-06-23T20:43:30.781Z