Universally Baire sets in $2^κ$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929644143378432 |
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| author | Ikegami, Daisuke Viale, Matteo |
| author_facet | Ikegami, Daisuke Viale, Matteo |
| contents | We generalize the basic theory of universally Baire sets of $2^ω$ to a theory of universally Baire subsets of $2^κ$. We show that the fundamental characterizations of the property of being universally Baire have natural generalizations that can be formulated also for subsets of $2^κ$, in particular we provide four equivalent uniform definitions in the parameter $κ$ (for $κ$ an infinite cardinal) characterizing for each such $κ$ the class of universally Baire subsets of $2^κ$. For $κ=ω$, these definitions bring us back to the original notion of universally Baire sets of reals given by Feng, Magidor and Woodin [2]. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16546 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universally Baire sets in $2^κ$ Ikegami, Daisuke Viale, Matteo Logic 03E57 (Primary) 03E15, 03E55 (Secondary) We generalize the basic theory of universally Baire sets of $2^ω$ to a theory of universally Baire subsets of $2^κ$. We show that the fundamental characterizations of the property of being universally Baire have natural generalizations that can be formulated also for subsets of $2^κ$, in particular we provide four equivalent uniform definitions in the parameter $κ$ (for $κ$ an infinite cardinal) characterizing for each such $κ$ the class of universally Baire subsets of $2^κ$. For $κ=ω$, these definitions bring us back to the original notion of universally Baire sets of reals given by Feng, Magidor and Woodin [2]. |
| title | Universally Baire sets in $2^κ$ |
| topic | Logic 03E57 (Primary) 03E15, 03E55 (Secondary) |
| url | https://arxiv.org/abs/2412.16546 |