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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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