Tree Properties at Successors of Singulars of Many Cofinalities
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866916595529416704 |
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| author | Adkisson, William |
| author_facet | Adkisson, William |
| contents | From many supercompact cardinals, we show that it is consistent for the tree property to hold at many small successors of singular cardinals, each with a different cofinality. In particular, we construct a model in which the tree property holds at $\aleph_{ω+ω+1}$ and at $\aleph_{ω_n+1}$ for all $0<n<ω$. We show that this can be done for the strong tree property as well, and extend the technique to large uncountable sequences of desired cofinalities. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_01762 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tree Properties at Successors of Singulars of Many Cofinalities Adkisson, William Logic 03E05 From many supercompact cardinals, we show that it is consistent for the tree property to hold at many small successors of singular cardinals, each with a different cofinality. In particular, we construct a model in which the tree property holds at $\aleph_{ω+ω+1}$ and at $\aleph_{ω_n+1}$ for all $0<n<ω$. We show that this can be done for the strong tree property as well, and extend the technique to large uncountable sequences of desired cofinalities. |
| title | Tree Properties at Successors of Singulars of Many Cofinalities |
| topic | Logic 03E05 |
| url | https://arxiv.org/abs/2502.01762 |