Preservation of splitting families and cardinal characteristics of the continuum
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2020
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| _version_ | 1866914757572820992 |
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| author | Goldstern, Martin Kellner, Jakob Mejía, Diego A. Shelah, Saharon |
| author_facet | Goldstern, Martin Kellner, Jakob Mejía, Diego A. Shelah, Saharon |
| contents | We show how to construct, via forcing, splitting families than are preserved by a certain type of finite support iterations. As an application, we construct a model where 15 classical characteristics of the continuum are pairwise different, concretely: the 10 (non-dependent) entries in Cichoń's diagram, $\mathfrak{m}(2\text{-Knaster})$, $\mathfrak{p}$, $\mathfrak{h}$, the splitting number $\mathfrak{s}$ and the reaping number $\mathfrak{r}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_13500 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Preservation of splitting families and cardinal characteristics of the continuum Goldstern, Martin Kellner, Jakob Mejía, Diego A. Shelah, Saharon Logic 03E17, 03E35, 03E40 We show how to construct, via forcing, splitting families than are preserved by a certain type of finite support iterations. As an application, we construct a model where 15 classical characteristics of the continuum are pairwise different, concretely: the 10 (non-dependent) entries in Cichoń's diagram, $\mathfrak{m}(2\text{-Knaster})$, $\mathfrak{p}$, $\mathfrak{h}$, the splitting number $\mathfrak{s}$ and the reaping number $\mathfrak{r}$. |
| title | Preservation of splitting families and cardinal characteristics of the continuum |
| topic | Logic 03E17, 03E35, 03E40 |
| url | https://arxiv.org/abs/2007.13500 |