The density zero ideal and the splitting number

Abstract

The main result of this paper is an improvement of the upper bound on the cardinal invariant cov⁎(Z0) that was discovered in [11]. Here Z0 is the ideal of subsets of the set of natural numbers that have asymptotic density zero. This improved upper bound is also dualized to get a better lower bound on the cardinal non⁎(Z0). En route some variations on the splitting number are introduced and several relationships between these variants are proved.