Superclub, splitting, separating statements
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909624178835456 |
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| author | Garti, Shimon Shelah, Saharon |
| author_facet | Garti, Shimon Shelah, Saharon |
| contents | We prove that superclub implies $\mathfrak{s}=\aleph_1$. More generally, superclub at a successor of a weakly compact cardinal implies $\mathfrak{s}_κ=κ^+$. Based on this statement, we separate tiltan from superclub at a successor of a supercompact cardinal. We use Galvin's property in order to separate tiltan from superclub at successors of both regular and singular cardinals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_00904 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Superclub, splitting, separating statements Garti, Shimon Shelah, Saharon Logic 03E02, 03E17 We prove that superclub implies $\mathfrak{s}=\aleph_1$. More generally, superclub at a successor of a weakly compact cardinal implies $\mathfrak{s}_κ=κ^+$. Based on this statement, we separate tiltan from superclub at a successor of a supercompact cardinal. We use Galvin's property in order to separate tiltan from superclub at successors of both regular and singular cardinals. |
| title | Superclub, splitting, separating statements |
| topic | Logic 03E02, 03E17 |
| url | https://arxiv.org/abs/2302.00904 |