English

Concentrated sets and $\gamma$-sets in the Miller model

General Topology 2024-06-24 v2

Abstract

Using combinatorial covering properties, we show that there is no concentrated set of reals of size ω2\omega_2 in the Miller model. The main result refutes a conjecture of Bartoszy\'{n}ski and Halbeisen. We also prove that there are no γ\gamma-set of reals of size ω2\omega_2 in the Miller model.

Cite

@article{arxiv.2310.03864,
  title  = {Concentrated sets and $\gamma$-sets in the Miller model},
  author = {Valentin Haberl and Piotr Szewczak and Lyubomyr Zdomskyy},
  journal= {arXiv preprint arXiv:2310.03864},
  year   = {2024}
}

Comments

arXiv admin note: text overlap with arXiv:2204.08257

R2 v1 2026-06-28T12:42:02.912Z