On the cofinality of the splitting number
Alan Dow, Saharon Shelah
TL;DR
This paper investigates the cofinality of the splitting number, demonstrating it can be singular, using a specialized forcing construction involving finite support matrix iterations of ccc posets.
Contribution
It introduces a novel forcing method with finite support matrix iterations to analyze the cofinality of the splitting number, extending previous techniques.
Findings
The splitting number can have singular cofinality.
A new forcing construction achieves the desired cofinality properties.
The method extends existing techniques for ultrafilter and splitting number analysis.
Abstract
The splitting number can be singular. The key method is to construct a forcing poset with finite support matrix iterations of ccc posets introduced by Blass and the second author "Ultrafilters with small generating sets", Israel J. Math., 65, (1989)
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