English

Menger and consonant sets in the Sacks model

Logic 2025-10-28 v3 General Topology

Abstract

Using iterated Sacks forcing and topological games, we prove that the existence of a totally imperfect Menger set in the Cantor cube with cardinality continuum is independent from ZFC. We also analyze the structure of Hurewicz and consonant subsets of the Cantor cube in the Sacks model.

Cite

@article{arxiv.2406.05457,
  title  = {Menger and consonant sets in the Sacks model},
  author = {Valentin Haberl and Piotr Szewczak and Lyubomyr Zdomskyy},
  journal= {arXiv preprint arXiv:2406.05457},
  year   = {2025}
}

Comments

26 pages

R2 v1 2026-06-28T16:58:12.426Z