2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225712We 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 pagesLogicGeneral Topology03C20, 03E04; 03C95, 54D20text