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

Lorenz Halbeisen; Silvan Horvath; Saharon Shelah

doi:10.1016/j.apal.2026.103747

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

Lorenz Halbeisen
, Silvan Horvath^*
, Saharon Shelah

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

We show that in the model obtained by iteratively pseudo-intersecting a Ramsey ultrafilter via a length-ω₂ countable support iteration of restricted Mathias forcing over a ground model satisfying 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^c-many near-coherence classes of ultrafilters.

Original language	English
Article number	103747
Journal	Annals of Pure and Applied Logic
Volume	177
Issue number	8
DOIs	https://doi.org/10.1016/j.apal.2026.103747
State	Published - 1 Aug 2026

Bibliographical note

Publisher Copyright:
© 2026 The Author(s)

Keywords

Mathias forcing
Q-point
Ramsey ultrafilter

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10.1016/j.apal.2026.103747

Cite this

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AB - We show that in the model obtained by iteratively pseudo-intersecting a Ramsey ultrafilter via a length-ω2 countable support iteration of restricted Mathias forcing over a ground model satisfying 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 2c-many near-coherence classes of ultrafilters.

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

Abstract

Bibliographical note

Keywords

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