The Baire and perfect set properties at singulars cardinals
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911983973957632 |
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| author | Dimonte, Vincenzo Poveda, Alejandro Thei, Sebastiano |
| author_facet | Dimonte, Vincenzo Poveda, Alejandro Thei, Sebastiano |
| contents | We construct a model of ZFC with a singular cardinal $κ$ such that every subset of $κ$ in $L(V_{κ+1})$ has both the $κ$-Perfect Set Property and the $\mathcal{\vec{U}}$-Baire Property. This is a higher analogue of Solovay's result for $L(\mathbb{R})$. We obtain this configuration starting with large-cardinal assumptions in the realm of supercompactness, thus improving former theorems by Cramer, Shi and Woodin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05973 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Baire and perfect set properties at singulars cardinals Dimonte, Vincenzo Poveda, Alejandro Thei, Sebastiano Logic We construct a model of ZFC with a singular cardinal $κ$ such that every subset of $κ$ in $L(V_{κ+1})$ has both the $κ$-Perfect Set Property and the $\mathcal{\vec{U}}$-Baire Property. This is a higher analogue of Solovay's result for $L(\mathbb{R})$. We obtain this configuration starting with large-cardinal assumptions in the realm of supercompactness, thus improving former theorems by Cramer, Shi and Woodin. |
| title | The Baire and perfect set properties at singulars cardinals |
| topic | Logic |
| url | https://arxiv.org/abs/2408.05973 |