On the number of $Q$-points

Silvan Horvath; Tan Özalp

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arXiv · 2608.08223

On the number of $Q$-points

Silvan Horvath·Tan Özalp

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Abstract

We show that, up to isomorphism, the number of $Q$-points is either finite, $2^{\mathfrak{d}}$ or $2^{\mathfrak{c}}$. This answers a question asked by Borodulin-Nadzieja, Mart\'{i}nez-Celis, Morawski and \'Swierczy\'nska, and by Halbeisen and the authors. We also show that under mild hypotheses, the existence of infinitely many $Q$-points implies the existence of non-atomic $Q$-measures, and of $2^{\mathfrak{c}}$-many Tukey-top $Q$-points, strengthening results of Raghavan and of Borodulin-Nadzieja et al..

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Silvan Horvath, Tan Özalp. 2026-08-08. On the number of $Q$-points. https://arxiv.org/abs/2608.08223

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