A Small Ultrafilter Number at Every Singular Cardinal
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908698618626048 |
|---|---|
| author | Benhamou, Tom Jirattikansakul, Sittinon |
| author_facet | Benhamou, Tom Jirattikansakul, Sittinon |
| contents | We obtain a small ultrafilter number at $\aleph_{ω_1}$. Moreover, we develop a version of the overlapping strong extender forcing with collapses which can keep the top cardinal $κ$ inaccessible. We apply this forcing to construct a model where $κ$ is the least inaccessible and $V_κ$ is a model of GCH at regulars, failures of SCH at singulars, and the ultrafilter numbers at all singulars are small. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07311 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A Small Ultrafilter Number at Every Singular Cardinal Benhamou, Tom Jirattikansakul, Sittinon Logic We obtain a small ultrafilter number at $\aleph_{ω_1}$. Moreover, we develop a version of the overlapping strong extender forcing with collapses which can keep the top cardinal $κ$ inaccessible. We apply this forcing to construct a model where $κ$ is the least inaccessible and $V_κ$ is a model of GCH at regulars, failures of SCH at singulars, and the ultrafilter numbers at all singulars are small. |
| title | A Small Ultrafilter Number at Every Singular Cardinal |
| topic | Logic |
| url | https://arxiv.org/abs/2302.07311 |