A unique $Q$-point and infinitely many near-coherence classes of ultrafilters
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918362087424000 |
|---|---|
| author | Halbeisen, Lorenz Horvath, Silvan Shelah, Saharon |
| author_facet | Halbeisen, Lorenz Horvath, Silvan Shelah, Saharon |
| contents | We show that in the model obtained by iteratively pseudo-intersecting a Ramsey ultrafilter via a length-$ω_2$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_17960 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A unique $Q$-point and infinitely many near-coherence classes of ultrafilters Halbeisen, Lorenz Horvath, Silvan Shelah, Saharon Logic 03E35 (Primary) 03E17 (Secondary) We show that in the model obtained by iteratively pseudo-intersecting a Ramsey ultrafilter via a length-$ω_2$ 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. |
| title | A unique $Q$-point and infinitely many near-coherence classes of ultrafilters |
| topic | Logic 03E35 (Primary) 03E17 (Secondary) |
| url | https://arxiv.org/abs/2505.17960 |