Sh:1265
- Halbeisen, L. J., Horvath, S., & Shelah, S. (2026). A unique Q-point and infinitely many near-coherence classes of ultrafilters. Ann. Pure Appl. Logic, 177(8), Paper No. 103747, 9. arXiv: 2505.17960 DOI: 10.1016/j.apal.2026.103747 MR: 5039973
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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. - Version 2026-02-27 (11p)
Bib entry
@article{Sh:1265,
author = {Halbeisen, Lorenz J. and Horvath, Silvan and Shelah, Saharon},
title = {{A unique $Q$-point and infinitely many near-coherence classes of ultrafilters}},
journal = {Ann. Pure Appl. Logic},
fjournal = {Annals of Pure and Applied Logic},
volume = {177},
number = {8},
year = {2026},
pages = {Paper No. 103747, 9},
issn = {0168-0072,1873-2461},
mrnumber = {5039973},
mrclass = {03E35 (03E17 54D80 91A44)},
doi = {10.1016/j.apal.2026.103747},
note = {\href{https://arxiv.org/abs/2505.17960}{arXiv: 2505.17960}},
arxiv_number = {2505.17960}
}