Geodesic
On the bounding, splitting, and distributivity numbers
Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 3, pp. 331-351.

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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).
DOI : 10.14712/1213-7243.2024.001
Classification : 03E15
Keywords: cardinal invariants of the continuum; matrix forcing 
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Dow, Alan; Shelah, Saharon. On the bounding, splitting, and distributivity numbers. Commentationes Mathematicae Universitatis Carolinae, Tome 64 (2023) no. 3, pp. 331-351. doi : 10.14712/1213-7243.2024.001. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2024.001/

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