The covering number and the uniformity of the ideal If

Let f, g is an element of (omega)omega. We will denote by g >> f that for every k < omega, f(n(k)) <= g(n) except for finitely many n. The ideal I-f on (omega)2 is the collection of sets X such that, for some g >> f and tau is an element of Pi(n <omega) (g(2))2, every x is an element of X satisfies tau(n) subset of x for infinitely many n. In the present paper, we will prove the consistency of cov(I-f) < c and non(I-f) < c. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.