The covering number and the uniformity of the ideal

摘要

Let f, g ∈~ω ω. We will denote by g f that for every k < ω, f (n~k) g (n) except for finitely many n. The ideal I_f on~ω 2 is the collection of sets X such that, for some g f and τ∈∏_n<ω g(n) 2, every x ∈ X satisfies τ(n) C x for infinitely many n . In the present paper, we will prove the consistency of cov(I_f) < c and non(I_f) < c.