Adding many Baumgartner clubs

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Abstract

I define a homogeneous 2–c.c. proper product forcing for adding many clubs of ω1 with finite conditions. I use this forcing to build models of b(ω1)=ℵ2, together with d(ω1) and 2ℵ0 large and with very strong failures of club guessing at ω1.
Original languageEnglish
Pages (from-to)797-810
Number of pages14
JournalArchive for Mathematical Logic
Volume56
Issue number7-8
Early online date9 May 2017
DOIs
Publication statusPublished - Nov 2017

Keywords

  • Baumgartner clubs
  • Strong failures of club guessing
  • Cardinal characteristics for ω1
  • Generalizations of Martin’s Axiom

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