Cardinal invariants related to density

2024/01/17 by DAVID VALDERRAMA, Valderrama, David · 1 citation
#03E17 #03E35 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2401.09649

Abstract

We investigate some variants of the splitting, reaping, and independence numbers defined using asymptotic density. Specifically, we give a proof of Con(\mathfraki<\mathfraks_1/2), Con(\mathfrakr_1/2<\mathfrakb) and Con(\mathfraki_*<2^ℵ₀). This answers two questions raised in arXiv:1808.02442v3. Besides, we prove the consistency of \mathfraks_1/2^∞ < non(E) and cov(E) < \mathfrakr_1/2^∞, where E is the σ-ideal generated by closed sets of measure zero.

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• Splitting Families, Reaping Families, and Families of Permutations Associated with Asymptotic Density

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