A connection between decomposable ultrafilters and possible cofinalities. II

Abstract

We use Shelah&#39;s theory of possible cofinalities in order to solve a problem about ultrafilters. THEOREM. Suppose that $ λ$ is a singular cardinal, $ λ&#39; < λ$, and the ultrafilter $D$ is $ κ$-decomposable for all regular cardinals $ κ$ with $ λ&#39; < κ< λ$. Then $D$ is either $ λ$-decomposable, or $ λ^+$-decomposable. We give applications to topological spaces and to abstract logics.