A Small Ultrafilter Number at Every Singular Cardinal
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866908698618626048 |
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| 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 |