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arXiv · 2505.17960

A unique $Q$-point and infinitely many near-coherence classes of ultrafilters

Lorenz Halbeisen·Silvan Horvath·Saharon Shelah
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Abstract

We show that in the model obtained by iteratively pseudo-intersecting a Ramsey ultrafilter via a length-$\omega_2$ countable support iteration of restricted Mathias forcing over a ground model satisfying $\textsf{CH}$, there is a unique $Q$-point up to isomorphism. In particular, it is consistent that there is only one $Q$-point while there are $2^{\mathfrak{c}}$-many near-coherence classes of ultrafilters.

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Lorenz Halbeisen, Silvan Horvath, Saharon Shelah. 2025-05-23. A unique $Q$-point and infinitely many near-coherence classes of ultrafilters. https://arxiv.org/abs/2505.17960

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