On the bounding, splitting, and distributivity numbers
Alan S. Dow, Saharon Shelah (2023)
Commentationes Mathematicae Universitatis Carolinae
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The cardinal invariants of are known to satisfy that . We prove that all inequalities can be strict. We also introduce a new upper bound for and show that it can be less than . 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).