Weak diamond and Galvin’s property

Shimon Garti*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

Let κ be an infinite cardinal, and 2κ<λ≤2κ+. We prove that if there is a weak diamond on κ+ then every {Cα:α<λ}⊆Dκ+ satisfies Galvin’s property. On the other hand, Galvin’s property is consistent with the failure of the weak diamond (and even with Martin’s axiom in the case of ℵ1). We derive some consequences about weakly inaccessible cardinals. We also prove that the negation of a similar property follows from the proper forcing axiom.

Original languageAmerican English
Pages (from-to)128-136
Number of pages9
JournalPeriodica Mathematica Hungarica
Volume74
Issue number1
DOIs
StatePublished - 1 Mar 2017

Bibliographical note

Publisher Copyright:
© 2016, Akadémiai Kiadó, Budapest, Hungary.

Keywords

  • Galvin’s property
  • Martin’s axiom
  • Proper forcing axiom
  • Weak diamond
  • Weakly inaccessible cardinals

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