13 citations · 36 across the 21 of their papers we have counts for
21 papers
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…
Cardinal invariants associated with the combinatorics of the uniformity number of the ideal of meager-additive sets
Miguel A. Cardona
In [CMRM24], it was proved that it is relatively consistent that \emph{bounding number} is smaller than the uniformity of , where denote…
Finitely additive measures on Boolean algebras
Miguel A. Cardona, Diego A. Mejía, Andrés F. Uribe-Zapata
In this article, we conduct a detailed study of \emph{finitely additive measures} (fams) in the context of Boolean algebras, focusing on three specific topics: freeness and approxi…
More separations of cardinal characteristics of the strong measure zero ideal
Miguel A. Cardona, Miroslav Repický, Saharon Shelah
Let be the -ideal of the null sets of reals. We introduce a new property of forcing notions that enable control of the additivity of after finite sup…
A general theory of iterated forcing using finitely additive measures
Miguel A. Cardona, Diego A. Mejía, Andrés F. Uribe-Zapata
Based on the work of Shelah, Kellner, and Tănasie (Fund. Math., 166(1-2):109-136, 2000 and Comment. Math. Univ. Carolin., 60(1):61-95, 2019), and the recent developments in the thi…
The cardinal characteristics of the ideal generated by the measure zero subsets of the reals
Miguel A. Cardona
Let be the ideal generated by the measure zero subsets of the reals. The purpose of this survey paper is to study the cardinal characteristics (the additivity,…
Soft-linkedness
Miguel A. Cardona
We have revised the softness property introduced by Jörg Brendle and Haim Judah (perfect sets of random reals. Israel J. Math., 83(1-2):153-176, 1993), to present a new definition…
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…
Separating cardinal characteristics of the strong measure zero ideal
Jörg Brendle, Miguel A. Cardona, Diego A. Mejía
Let be the -ideal of the strong measure zero sets of reals. We present general properties of forcing notions that allow to control of the additivity of $\mathcal{…
Localization and anti-localization cardinals
Miguel A. Cardona, Diego Alejandro Mejía
This paper is intended to survey the basics of localization and anti-localization cardinals on the reals, and its interplay with notions and cardinal characteristics related to mea…
More about the cofinality and the covering of the ideal of strong measure zero sets
Miguel A. Cardona, Diego A. Mejía
We improve the previous work of Yorioka and the first author about the combinatorics of the ideal of strong measure zero sets of reals. We refine the notions of domi…
A friendly iteration forcing that the four cardinal characteristics of can be pairwise different
Miguel A. Cardona
Let be the -ideal generated by the closed measure zero sets of reals. We use an ultrafilter-extendable matrix iteration of ccc posets to force that, for $\mathcal{…
Forcing constellations of Cichoń's diagram by using the Tukey order
Miguel A. Cardona, Diego A. Mejía
We use known finite support iteration techniques to present various examples of models where several cardinal characteristics of Cichoń's diagram are pairwise different. We show so…
Continuum Many Different Things: Localisation, Anti-Localisation and Yorioka Ideals
Miguel Antonio Cardona, Lukas Daniel Klausner, Diego Alejandro Mejía
Combining creature forcing approaches from arXiv:1003.3425 and arXiv:1402.0367, we show that, under CH, there is a proper -bounding poset with -cc that forces contin…
Tukey-order with models on Pawlikowski's theorems
Miguel A. Cardona
In J. Symbolic Logic,51(4): 957-968, 1986, Pawlikowski proved that, if is a random real over , and is Cohen real over , then (a) in $\mathbf{N}[r…
Cohen real or random real: effect on strong measure zero sets and strongly meager sets
Miguel A. Cardona
We show that the set of the ground-model reals has strong measure zero (is strongly meager) after adding a single Cohen real (random real). As consequence we prove that the set of…
On cardinal characteristics associated with the strong measure zero ideal
Miguel A. Cardona
Let be the strong measure zero -ideal. We prove a result providing bounds for which implies Yorioka's characterization of the cofinal…
Yorioka's characterization of the cofinality of the strong measure zero ideal and its independency from the continuum
Miguel A. Cardona
In this paper we present a simpler proof of the fact that no inequality between and can be decided in ZFC by using well-known tecniques…
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…
Filter-linkedness and its effect on preservation of cardinal characteristics
Jörg Brendle, Miguel A. Cardona, Diego A. Mejía
We introduce the property ``-linked'' of subsets of posets for a given free filter on the natural numbers, and define the properties ``--linked'' and ``--Knaster…
On cardinal characteristics of Yorioka ideals
Miguel A. Cardona, Diego A. Mejía
Yorioka [J. Symbolic Logic 67(4):1373-1384, 2002] introduced a class of ideals (parametrized by reals) on the Cantor space to prove that the relation between the size of the contin…