The density zero ideal and the splitting number

Annals of Pure and Applied Logic 171 (7):102807 (2020)
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Abstract

The main result of this paper is an improvement of the upper bound on the cardinal invariant $cov^*(L_0)$ that was discovered in [11]. Here $L_0$ 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 $non^*(L_0)$. En route some variations on the splitting number are introduced and several relationships between these variants are proved.

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References found in this work

Souslin forcing.Jaime I. Ihoda & Saharon Shelah - 1988 - Journal of Symbolic Logic 53 (4):1188-1207.
Sticks and clubs.Sakaé Fuchino, Saharon Shelah & Lajos Soukup - 1997 - Annals of Pure and Applied Logic 90 (1-3):57-77.
Combinatorics for the dominating and unsplitting numbers.Jason Aubrey - 2004 - Journal of Symbolic Logic 69 (2):482-498.

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