On a theorem by Juhász and Szentmiklóssy

Abstract

We extend a theorem by Juhász and Szentmiklóssy to notions related to pseudocompactness. We also allow the case when one of the cardinals under consideration is singular. We give an application to the study of decomposable ultrafilters: if κ is singular, D is a uniform ultrafilter over κ^+, and D' is a uniform ultrafilter over cf κ, then D' \times D is κ-decomposable.

arXiv commentv2, added a section on decomposabilty of ultrafilters, various other improvements