Disjoint Stationary Sequences on an Interval of Cardinals
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916896794738688 |
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| author | Jakob, Hannes |
| author_facet | Jakob, Hannes |
| contents | We answer a question of Krueger by obtaining -- from countably many Mahlo cardinals -- a model where there is a disjoint stationary sequence on $\aleph_{n+2}$ for every $n\inω$. In that same model, the notions of being internally stationary and internally club are distinct on a stationary subset of $[H(Θ)]^{\aleph_{n+1}}$ for every $n\inω$ and $Θ\geq\aleph_{n+2}$, answering another of Krueger's questions. This is obtained by employing a product of variants of Mitchell forcing which uses finite support for the Cohen reals and full support for the countably many collapses. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_01986 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Disjoint Stationary Sequences on an Interval of Cardinals Jakob, Hannes Logic 03E05 (Primary) 03E35, 03E55 (Secondary) We answer a question of Krueger by obtaining -- from countably many Mahlo cardinals -- a model where there is a disjoint stationary sequence on $\aleph_{n+2}$ for every $n\inω$. In that same model, the notions of being internally stationary and internally club are distinct on a stationary subset of $[H(Θ)]^{\aleph_{n+1}}$ for every $n\inω$ and $Θ\geq\aleph_{n+2}$, answering another of Krueger's questions. This is obtained by employing a product of variants of Mitchell forcing which uses finite support for the Cohen reals and full support for the countably many collapses. |
| title | Disjoint Stationary Sequences on an Interval of Cardinals |
| topic | Logic 03E05 (Primary) 03E35, 03E55 (Secondary) |
| url | https://arxiv.org/abs/2309.01986 |