On the bounding, splitting, and distributivity numbers

Alan Dow; Saharon Shelah

doi:10.14712/1213-7243.2024.001

On the bounding, splitting, and distributivity numbers

Alan Dow, Saharon Shelah

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The cardinal invariants h, b, s of P(ω) are known to satisfy that ω₁ ≤ h ≤ min{b, s}. We prove that all inequalities can be strict. We also introduce a new upper bound for h and show that it can be less than 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).

Original language	English
Pages (from-to)	331-351
Number of pages	21
Journal	Commentationes Mathematicae Universitatis Carolinae
Volume	64
Issue number	3
DOIs	https://doi.org/10.14712/1213-7243.2024.001
State	Published - 2023

Bibliographical note

Publisher Copyright:
© (2023), (Charles University, Faculty of Mathematics and Physics). All rights reserved.

Keywords

cardinal invariants of the continuum
matrix forcing

Access to Document

10.14712/1213-7243.2024.001

Cite this

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On the bounding, splitting, and distributivity numbers

Abstract

Bibliographical note

Keywords

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