This research demonstrates an ideal on ω that is not katetov below nwd and explores implications for ideals.
We provide a counterexample to the Category Dichotomy in the framework of ZFC. That is, we prove the existence of an ideal on ω that is not Kat{e}tov below nwd and does not have restrictions above ED. We also prove that in the Laver model every tall P-ideal is Kat{e}tov-Blass above EDfin and that it is consistent that every Q⁺ ideal is meager.
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Dow et al. (2025) studied this question.
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