Uniformity numbers of the null-additive and meager-additive ideals
Logic
2025-09-30 v3
Abstract
Denote by and the ideals of null-additive and meager-additive subsets of~, respectively. We prove in ZFC that and introduce a new (Polish) relational system to reformulate Bartoszy\'nski's and Judah's characterization of the uniformity of , which is helpful to understand the combinatorics of and to prove consistency results. As for the latter, we prove that (even ) is consistent with ZFC, as well as several constellations of Cicho\'n's diagram with , and , which include and .
Cite
@article{arxiv.2401.15364,
title = {Uniformity numbers of the null-additive and meager-additive ideals},
author = {Miguel A. Cardona and Diego A. Mejía and Ismael E. Rivera-Madrid},
journal= {arXiv preprint arXiv:2401.15364},
year = {2025}
}
Comments
Final version