Article
| Title: | On the bounding, splitting, and distributivity numbers (English) |
| Author: | Dow, Alan |
| Author: | Shelah, Saharon |
| Language: | English |
| Journal: | Commentationes Mathematicae Universitatis Carolinae |
| ISSN: | 0010-2628 (print) |
| ISSN: | 1213-7243 (online) |
| Volume: | 64 |
| Issue: | 3 |
| Year: | 2023 |
| Pages: | 331-351 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | The cardinal invariants $ \mathfrak h, \mathfrak b,\mathfrak s$ of $ \mathcal P (\omega)$ are known to satisfy that $\omega_1 \leq \mathfrak h \leq\min\{\mathfrak b, \mathfrak s\}$. We prove that all inequalities can be strict. We also introduce a new upper bound for $\mathfrak h$ and show that it can be less than $\mathfrak s$. The key method is to utilize finite support matrix iterations of ccc posets following paper Ultrafilters with small generating sets by A. Blass and S. Shelah (1989). (English) |
| Keyword: | cardinal invariants of the continuum |
| Keyword: | matrix forcing |
| MSC: | 03E15 |
| idZBL: | Zbl 07830512 |
| idMR: | MR4717505 |
| DOI: | 10.14712/1213-7243.2024.001 |
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| Date available: | 2024-03-18T10:43:37Z |
| Last updated: | 2024-08-02 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152302 |
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