A connection between decomposable ultrafilters and possible cofinalities. II
Abstract
Description
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.
6 pages
6 pages