Uniformity numbers of the null-additive and meager-additive ideals

2024/01/27 by Cardona, Miguel A., Mejía, Diego A., Rivera-Madrid, Ismael E. · 2 citations
#03E05 #03E17 #03E35 #03E40 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2401.15364

Abstract

Denote by NA and MA the ideals of null-additive and meager-additive subsets of~2^ω, respectively. We prove in ZFC that add(NA)=non(NA) and introduce a new (Polish) relational system to reformulate Bartoszyński's and Judah's characterization of the uniformity of MA, which is helpful to understand the combinatorics of MA and to prove consistency results. As for the latter, we prove that cov(MA)<\mathfrakc (even cov(MA)<non(N)) is consistent with ZFC, as well as several constellations of Cichoń's diagram with non(NA), non(MA) and add(SN), which include non(NA)<\mathfrakb< non(MA) and \mathfrakb< add(SN)<cov(M)<\mathfrakd=\mathfrakc.

Cited by

• Directed schemes of ideals and cardinal characteristics, I: the meager additive ideal
• Constant prediction and evasion number, I: Generalization and variants

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