Generically extendible cardinals
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916493283819520 |
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| author | Usuba, Toshimichi |
| author_facet | Usuba, Toshimichi |
| contents | In this paper, we study the notion of a generically extendible cardinal, which is a generic version of an extendible cardinal. We prove that the generic extendibility of $ω_1$ or $ω_2$ has small consistency strength, but that of a cardinal $>ω_2$ does not. We also consider some results concerned with generically extendible cardinals, such as indestructibility, generic absoluteness of the reals, and Boolean valued second order logic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_12144 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Generically extendible cardinals Usuba, Toshimichi Logic 03E40, 03E55, 03E57 In this paper, we study the notion of a generically extendible cardinal, which is a generic version of an extendible cardinal. We prove that the generic extendibility of $ω_1$ or $ω_2$ has small consistency strength, but that of a cardinal $>ω_2$ does not. We also consider some results concerned with generically extendible cardinals, such as indestructibility, generic absoluteness of the reals, and Boolean valued second order logic. |
| title | Generically extendible cardinals |
| topic | Logic 03E40, 03E55, 03E57 |
| url | https://arxiv.org/abs/2209.12144 |