The covering number and the uniformity of the ideal ℐf.

Let f, g ∈ ωω . We will denote by g ≫ f that for every k < ω, f (nk) ≤ g (n ) except for finitely many n . The ideal ℐf on ω2 is the collection of sets X such that, for some g ≫ f and τ ∈ ∏n <ωg (n )2, every x ∈ X satisfies τ (n ) ⊂ x for infinitely many n . In the present paper, we will prove the consistency of cov(ℐf) < &cfr; and non(ℐf) < &cfr;. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]