A connection between decomposable ultrafilters and possible cofinalities. II

Paolo Lipparini

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arXiv · math/0605022

A connection between decomposable ultrafilters and possible cofinalities. II

Paolo Lipparini

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Abstract

We use Shelah's theory of possible cofinalities in order to solve a problem about ultrafilters. THEOREM. Suppose that $ λ$ is a singular cardinal, $ λ' < λ$, and the ultrafilter $D$ is $ κ$-decomposable for all regular cardinals $ κ$ with $ λ' < κ< λ$. Then $D$ is either $ λ$-decomposable, or $ λ^+$-decomposable. We give applications to topological spaces and to abstract logics.

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BibTeX RIS

Paolo Lipparini. 2006-04-30. A connection between decomposable ultrafilters and possible cofinalities. II. https://arxiv.org/abs/math/0605022

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