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.
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