Stationary Reflection and the Failure OF SCH at $\aleph_{ω_1}$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910712043929600 |
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| author | Benhamou, Tom Sinapova, Dima |
| author_facet | Benhamou, Tom Sinapova, Dima |
| contents | Combining stationary reflection (a compactness property) with the failure of SCH (an instance of non-compactness) has been a long-standing theme. We obtain this at $\aleph_{ω_1}$, answering a question of Ben-Neria, Hayut, and Unger: We prove from the existence of uncountably many supercompact cardinals the consistency of $\aleph_{ω_1}$ is strong limit together with $2^{\aleph_{ω_1}}>\aleph_{ω_1+1}$ and every stationary set of $\aleph_{ω_1+1}$ reflects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09048 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Stationary Reflection and the Failure OF SCH at $\aleph_{ω_1}$ Benhamou, Tom Sinapova, Dima Logic Combining stationary reflection (a compactness property) with the failure of SCH (an instance of non-compactness) has been a long-standing theme. We obtain this at $\aleph_{ω_1}$, answering a question of Ben-Neria, Hayut, and Unger: We prove from the existence of uncountably many supercompact cardinals the consistency of $\aleph_{ω_1}$ is strong limit together with $2^{\aleph_{ω_1}}>\aleph_{ω_1+1}$ and every stationary set of $\aleph_{ω_1+1}$ reflects. |
| title | Stationary Reflection and the Failure OF SCH at $\aleph_{ω_1}$ |
| topic | Logic |
| url | https://arxiv.org/abs/2411.09048 |