Avoiding Families and Tukey Functions on the Nowhere Dense Ideal
نویسندگان
چکیده
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 2N with the property that for each nowhere dense subset of 2N there is a set in F not intersecting it. We call such families avoiding.
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