Avoiding families and Tukey functions on the nowhere-dense ideal

Slawomir Solecki, Stevo Todorcevic

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate Tukey functions from the ideal of all closed nowhere-dense subsets of 2N. In particular, we answer an old question of Isbell and Fremlin by showing that this ideal is not Tukey reducible to the ideal of density zero subsets of N. We also prove non-existence of various special types of Tukey reductions from the nowhere-dense ideal to analytic P-ideals. In connection with these results, we study families F of clopen subsets of 2 N with the property that for each nowhere-dense subset of 2 N there is a set in F not intersecting it. We call such families avoiding.

Original languageEnglish (US)
Pages (from-to)405-435
Number of pages31
JournalJournal of the Institute of Mathematics of Jussieu
Volume10
Issue number2
DOIs
StatePublished - Apr 1 2011

Keywords

  • Tukey reductions
  • analytic P-ideals
  • nowhere-dense sets

ASJC Scopus subject areas

  • Mathematics(all)

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