Anatomy of $\tilde{\mathbb{E}}$
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916117624127488 |
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| author | Mejía, Diego A. |
| author_facet | Mejía, Diego A. |
| contents | We present a detailed general framework to describe the forcing $\tilde{\mathbb{E}}$, defined by Kellner, Shelah and Tanăsie to prove the consistency with ZFC of an alternative order of Cichoń's maximum. Our presentation is close to the framework of tree-creature forcing notions from Horowitz and Shelah. We show that the posets in this class have strong FAM limits for intervals (in recent terminology, they are $σ$-FAM-linked) and, furthermore, that they also have strong ultrafilter limits for intervals. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_04706 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anatomy of $\tilde{\mathbb{E}}$ Mejía, Diego A. Logic 03E40, 28A12, 28A25 We present a detailed general framework to describe the forcing $\tilde{\mathbb{E}}$, defined by Kellner, Shelah and Tanăsie to prove the consistency with ZFC of an alternative order of Cichoń's maximum. Our presentation is close to the framework of tree-creature forcing notions from Horowitz and Shelah. We show that the posets in this class have strong FAM limits for intervals (in recent terminology, they are $σ$-FAM-linked) and, furthermore, that they also have strong ultrafilter limits for intervals. |
| title | Anatomy of $\tilde{\mathbb{E}}$ |
| topic | Logic 03E40, 28A12, 28A25 |
| url | https://arxiv.org/abs/2402.04706 |