相关论文: On cardinal characteristics of Yorioka ideals

Let $\mathcal{SN}$ be the strong measure zero $\sigma$-ideal. We prove a result providing bounds for $\mathrm{cof}(\mathcal{SN})$ which implies Yorioka's characterization of the cofinality of the strong measure zero. In addition, we use…

Using a countable support product of creature forcing posets, we show that consistently, for uncountably many different functions the associated Yorioka ideals' uniformity numbers can be pairwise different. In addition we show that, in the…

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 measure zero sets. We prove general theorems for directed…

Combining creature forcing approaches from arXiv:1003.3425 and arXiv:1402.0367, we show that, under CH, there is a proper $\omega^\omega$-bounding poset with $\aleph_2$-cc that forces continuum many pairwise different cardinal…

We improve the previous work of Yorioka and the first author about the combinatorics of the ideal $\mathcal{SN}$ of strong measure zero sets of reals. We refine the notions of dominating systems of the first author and introduce the new…

We introduce a two-parameter modification of the cofinality invariant of ideals. This allows us to include the interaction of a pair of ideals in the study of base-like structures. We find the values (cardinal numbers or well-known cardinal…

In this paper we present a simpler proof of the fact that no inequality between $\mathrm{cof}(\mathcal{SN})$ and $\mathfrak{c}$ can be decided in ZFC by using well-known tecniques and results.

Let $\mathcal{E}$ be the $\sigma$-ideal generated by the closed measure zero sets of reals. We use an ultrafilter-extendable matrix iteration of ccc posets to force that, for $\mathcal{E}$, their associated cardinal characteristics (i.e.\…

Let $\mathcal{E}$ be the ideal generated by the $F_\sigma$ measure zero subsets of the reals. The purpose of this survey paper is to study the cardinal characteristics (the additivity, covering number, uniformity, and cofinality) of…

Let $\mathcal{SN}$ be the $\sigma$-ideal of the strong measure zero sets of reals. We present general properties of forcing notions that allow to control of the additivity of $\mathcal{SN}$ after finite support iterations. This is applied…

We consider cardinal invariants determined from Hausdorff measures. We separate many cardinal invariants of Hausdorff measure $0$ ideals using two models that separate many cardinal invariants of Yorioka ideals at once from earlier work.…

Inspired by Bartoszy\'nski's work on small sets, we introduce a new ideal defined by interval partitions on natural numbers and summable sequences of positive reals. Similarly, we present another ideal that relies on Bartoszy\'nski's and…

Let $\mathcal{N}$ be the $\sigma$-ideal of the null sets of reals. We introduce a new property of forcing notions that enable control of the additivity of $\mathcal{N}$ after finite support iterations. This is applied to answer some open…

Generalizing Keisler's notion of regularity for ultrafilters, Taylor introduced degrees of regularity for ideals and showed that a countably complete nonregular ideal on $\omega_1$ must be somewhere $\omega_1$-dense. We prove a dichotomy…

We study variants of classical Laver forcing defined from co-ideals and analyze their combinatorial properties in terms of the Kat\v{e}tov order. In particular, we give a Kat\v{e}tov-theoretic characterization of when Laver forcing…

We propose a reformulation of the ideal $\mathcal{N}$ of Lebesgue measure zero sets of reals modulo an ideal $J$ on $\omega$, which we denote by $\mathcal{N}_J$. In the same way, we reformulate the ideal $\mathcal{E}$ generated by…

For a strongly inacessible cardinal $\kappa$, we investigate the relationships between the following ideals: - the ideal of meager sets in the ${<}\kappa$-box product topology - the ideal of "null" sets in the sense of [Sh:1004]…

For each countable ordinal $\alpha \ge 2$, the ideals $\mathsf{conv}_\alpha$ were introduced in ``Critical ideals for countable compact spaces'' (to appear in Fund. Math., see also arXiv:2503.12571) to characterize compact countable spaces…

In their recent paper on posets with a pseudocomplementation denoted by * the first and the third author introduced the concept of a *-ideal. This concept is in fact an extension of a similar concept introduced in distributive…

The notion of Igusa-Todorov classes is introduced in connection with the finitistic dimension conjecture. As application we consider conditions on special ideals which imply the Igusa-Todorov and other finiteness conditions on modules…