arXiv subjects

Raul Figueroa-Sierra

Publications and source records attributed to Raul Figueroa-Sierra.

2 recordsLinked to original sources

arXiv2026

Are scales Fréchet?

We continue the study of Dow spaces of a $\mathfrak{b}$-scale, originally introduced by Alan Dow in "$π$-Weight and the Fréchet-Urysohn property" (Topology and its Applications, Vol. 174, pp. 56-61). We prove that it is consistent that all such spaces are Fréchet, but it is also consistent that none of them is. We use these spaces to exhibit (consistently) a $\triangle_{2}^{1}$ ideal that does not satisfy the Category Dichotomy. Finally, we prove that the Category Dichotomy holds for all co-analytic ideals.

math.GN↗

arXiv2025

The Category Dichotomy for Ideals

We provide a counterexample to the Category Dichotomy in the framework of $\textsf{ZFC}$. That is, we prove the existence of an ideal on $ω$ that is not Katětov below $\mathsf{nwd}$ and does not have restrictions above $\mathcal{ED}$. We also prove that in the Laver model every tall $\mathsf{P}$-ideal is Katětov-Blass above $\mathcal{ED}_{\mathsf{fin}}$ and that it is consistent that every $\mathsf{Q}^{+}$ ideal is meager.

math.LO↗