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arXiv · 2503.02290

The Category Dichotomy for Ideals

Alan Dow·Raul Figueroa-Sierra·Osvaldo Guzmán·Michael Hrušák
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Abstract

We provide a counterexample to the Category Dichotomy in the framework of $\textsf{ZFC}$. That is, we prove the existence of an ideal on $\omega$ that is not Kat\v{e}tov 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 Kat\v{e}tov-Blass above $\mathcal{ED}_{\mathsf{fin}}$ and that it is consistent that every $\mathsf{Q}^{+}$ ideal is meager.

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Alan Dow, Raul Figueroa-Sierra, Osvaldo Guzmán, Michael Hrušák. 2025-03-04. The Category Dichotomy for Ideals. https://doi.org/10.1016/j.apal.2025.103717

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