Several comments about the combinatorics of τ-covers

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Abstract

In a previous work with Mildenberger and Shelah, we showed that the combinatorics of the selection hypotheses involving τ-covers is sensitive to the selection operator used. We introduce a natural generalization of Scheepers' selection operators, and show that: (1) A slight change in the selection operator, which in classical cases makes no difference, leads to different properties when τ-covers are involved. (2) One of the newly introduced properties sheds some light on a problem of Scheepers concerning τ-covers. Improving an earlier result, we also show that no generalized Luzin set satisfies Ufin(Γ,T).

Original languageEnglish
Pages (from-to)47-53
Number of pages7
JournalNote di Matematica
Volume27
Issue numberSUPPL1
StatePublished - 2007

Keywords

  • Borel covers
  • Combinatorial cardinal characteristics of the continuum
  • Open covers
  • Selection principles
  • γ-cover
  • τ-cover
  • ω-cover

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