Authors: Solecki, Slawomir
Todorčević, Stevo 
Title: Avoiding families and Tukey functions on the nowhere-dense ideal
Journal: Journal of the Institute of Mathematics of Jussieu
Volume: 10
Issue: 2
First page: 405
Last page: 435
Issue Date: 1-Apr-2011
ISSN: 1474-7480
DOI: 10.1017/S1474748010000277
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.
Keywords: analytic P-ideals | nowhere-dense sets | Tukey reductions
Publisher: Cambridge University Press
Project: NSF, Grant DMS-0700841

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