Abstract
We use Shelah's theory of possible cofinalities in order to solve some problems about ultrafilters. Theorem: Suppose that is a singular cardinal, , and the ultrafilter is -decomposable for all regular cardinals with . Then is either -decomposable or -decomposable. Corollary: If is a singular cardinal, then an ultrafilter is (,)-regular if and only if it is either -decomposable or -decomposable. We also give applications to topological spaces and to abstract logics.
Citation
Paolo Lipparini. "Decomposable Ultrafilters and Possible Cofinalities." Notre Dame J. Formal Logic 49 (3) 307 - 312, 2008. https://doi.org/10.1215/00294527-2008-014
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