English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We improve the previous work of Yorioka and the first author about thecombinatorics of the ideal $\mathcal{SN}$ of strong measure zero sets of reals.We refine the notions of dominating systems of the first author and introducethe new combinatorial principle $\mathrm{DS}(\delta)$ that helps to find simpleconditions to deduce $\mathfrak{d}_\kappa \leq \mathrm{cof}(\mathcal{SN})$(where $\mathfrak{d}_\kappa$ is the dominating number on $\kappa^\kappa$). Inaddition, we find a new upper bound of $\mathrm{cof}(\mathcal{SN})$ by usingproducts of relational systems and cardinal characteristics associated withYorioka ideals. In addition, we dissect and generalize results from Pawlikowskito force upper bounds of the covering of $\mathcal{SN}$, particularly forfinite support iterations of precaliber posets.  Finally, as applications of our main theorems, we prove consistency resultsabout the cardinal characteristics associated with $\mathcal{SN}$ and theprinciple $\mathrm{DS}(\delta)$. For example, we show that$\mathrm{cov}(\mathcal{SN})<\mathrm{non}(\mathcal{SN})=\mathfrak{c}<\mathrm{cof}(\mathcal{SN})$holds in Cohen model, and we refine a result (and the proof) of the firstauthor about the consistency of$\mathrm{cov}(\mathcal{SN})<\mathrm{non}(\mathcal{SN})<\mathrm{cof}(\mathcal{SN})$,with $\mathfrak{c}$ in any desired position with respect to$\mathrm{cof}(\mathcal{SN})$, and the improvement that$\mathrm{non}(\mathcal{SN})$ can be singular here.

More about the cofinality and the covering of the ideal of strong measure zero sets