English

Fin-intersecting MAD families

General Topology 2023-04-26 v2

Abstract

We introduce a new class of almost disjoint families which we call fin-intersecting almost disjoint families. They are related to almost disjoint families whose Vietoris Hyperspace of their Isbell-Mr\'owka spaces are pseudocompact. We show that under p=c\mathfrak p=\mathfrak c fin-intersecting MAD families exist generically and they also exist if a<s\mathfrak{a<s}, but that there are also non fin-intersecting MAD families in ZFC. We also show that under CH, there exists fin intersecting MAD families which remain like that after adding an arbitrary quantity of Cohen reals and Random reals. These results give more models in which pseudocompact MAD families exist.

Keywords

Cite

@article{arxiv.2212.01484,
  title  = {Fin-intersecting MAD families},
  author = {Cesar Corral and Vinicius de O. Rodrigues},
  journal= {arXiv preprint arXiv:2212.01484},
  year   = {2023}
}

Comments

22 pages

R2 v1 2026-06-28T07:20:58.966Z