On a theorem by Juhász and Szentmiklóssy

2013/05/08 by Paolo Lipparini, Lipparini, Paolo
Mathematics · #03E05 #03E75 #54A20 #54D20 #FOS: Mathematics #General Topology (math.GN) #math.GN #msc:03E05 #msc:03E75 #msc:54A20 #msc:54D20

paper · pdf · doi:10.48550/arxiv.1305.1794

v2, added a section on decomposabilty of ultrafilters, various other improvements

arxiv created 2013/05/22 · arxiv updated 2013/05/23

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' × D is κ-decomposable.

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