On compactness of weak square at singulars of uncountable cofinality
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917309837213696 |
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| author | Levine, Maxwell |
| author_facet | Levine, Maxwell |
| contents | Cummings, Foreman, and Magidor proved that Jensen's square principle is non-compact at $\aleph_ω$, meaning that it is consistent that $\square_{\aleph_n}$ holds for all $n<ω$ while $\square_{\aleph_ω}$ fails. We investigate the natural question of whether this phenomenon generalizes to singulars of uncountable cofinality. Surprisingly, we show that under some mild hypotheses, the weak square principle $\square_κ^*$ is in fact compact at singulars of uncountable cofinality, and that an even stronger version of these hypotheses is not enough for compactness of weak square at $\aleph_ω$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_09380 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On compactness of weak square at singulars of uncountable cofinality Levine, Maxwell Logic 03E04 (Primary) 03E35, 03E55 (Secondary) Cummings, Foreman, and Magidor proved that Jensen's square principle is non-compact at $\aleph_ω$, meaning that it is consistent that $\square_{\aleph_n}$ holds for all $n<ω$ while $\square_{\aleph_ω}$ fails. We investigate the natural question of whether this phenomenon generalizes to singulars of uncountable cofinality. Surprisingly, we show that under some mild hypotheses, the weak square principle $\square_κ^*$ is in fact compact at singulars of uncountable cofinality, and that an even stronger version of these hypotheses is not enough for compactness of weak square at $\aleph_ω$. |
| title | On compactness of weak square at singulars of uncountable cofinality |
| topic | Logic 03E04 (Primary) 03E35, 03E55 (Secondary) |
| url | https://arxiv.org/abs/2208.09380 |