On Cohen and Prikry Forcing Notions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866913357246758912 |
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| author | Benhamou, Tom Gitik, Moti |
| author_facet | Benhamou, Tom Gitik, Moti |
| contents | We show that it is possible to add $κ^+-$Cohen subsets to $κ$ with a Prikry forcing over $κ$. This answers a question from \cite{HayutBenhanouGitik}. A strengthening of non-Galvin property is introduced. It is shown to be consistent using a single measurable cardinal which improves a previous result by S. Garti, S. Shelah, and the first author \cite{BenhamouGartieShelah}. A situation with extender-based Prikry forcings is examined. This relates to a question of H. Woodin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_02860 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Cohen and Prikry Forcing Notions Benhamou, Tom Gitik, Moti Logic We show that it is possible to add $κ^+-$Cohen subsets to $κ$ with a Prikry forcing over $κ$. This answers a question from \cite{HayutBenhanouGitik}. A strengthening of non-Galvin property is introduced. It is shown to be consistent using a single measurable cardinal which improves a previous result by S. Garti, S. Shelah, and the first author \cite{BenhamouGartieShelah}. A situation with extender-based Prikry forcings is examined. This relates to a question of H. Woodin. |
| title | On Cohen and Prikry Forcing Notions |
| topic | Logic |
| url | https://arxiv.org/abs/2204.02860 |