More on the density zero ideal

2017/12/08 by Raghavan, Dilip
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1712.03308

Abstract

The main result of this paper is an improvement of the upper bound on the cardinal invariant \mathordcov^∗(Z₀) that was discovered by Raghavan and Shelah in an earlier paper. 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 \mathordnon^∗(Z₀). En route some variations on the splitting number are introduced and several relationships between these variants are proved.

Related

• Cardinal invariants related to density
• Two inequalities between cardinal invariants
• A note on asymptotic density
• Splitting Families, Reaping Families, and Families of Permutations Associated with Asymptotic Density
• On cardinal characteristics associated with the strong measure zero ideal