3 papers
math.LO2025
Directed schemes of ideals and cardinal characteristics, I: the meager additive ideal
Miguel A. Cardona, Diego A. Mejía, Ismael E. Rivera-Madrid
We introduce the notion of directed scheme of ideals to characterize peculiar ideals on the reals, which comes from a formalization of the framework of Yorioka ideals for strong me…
math.LO2024
Uniformity numbers of the null-additive and meager-additive ideals
Miguel A. Cardona, Diego A. Mejía, Ismael E. Rivera-Madrid
Denote by and the ideals of null-additive and meager-additive subsets of~, respectively. We prove in ZFC that $\mathrm{add}(\mathcal{NA})=\mathrm…
math.LO2019
The covering number of the strong measure zero ideal can be above almost everything else
Miguel A. Cardona, Diego A. Mejía, Ismael E. Rivera-Madrid
We show that certain type of tree forcings, including Sacks forcing, increases the covering of the strong measure zero ideal . As a consequence, in Sacks model, such…