发表机构
Wrocław University of Science and Technology（弗罗茨瓦夫科技大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究贫集与闭测度零集平移的组合性质，探讨相关Borel猜想，获得贫理想可加性新刻画，并证明若干基数不变量关系。
AI 中文摘要
我们研究贫集与闭测度零集的平移组合性质。我们讨论相关小集类的Borel猜想格局，并证明在Miller模型中不存在不可数的零可加集。我们还研究这些类的基数不变量。特别地，我们考察与贫可加集相关的σ-理想$\mathcal{H}_{F}$的基数不变量。我们获得贫理想可加性的一个新刻画，并回答了Cardona的一些问题。我们还证明$\mathrm{non}(\mathcal{E}^{*})$（等于理想$\mathcal{E}$的覆盖数的平移版本）接近于与Laver性质相关的基数不变量。这加强了Bartoszyński和Judah以及Elekes和Steprāns的结果。最后，我们证明每个$\mathcal{E}$-Luzin集都属于$\mathcal{E}^{*}$。
英文摘要
We study combinatorial properties of translations of meager and closed sets of measure zero. We discuss constellations of Borel conjectures for related classes of small sets and show that there are no uncountable null-additive sets in the Miller model. We also study cardinal invariants of those classes. In particular, we investigate the cardinal invariants of $σ$-ideals $\mathcal{H}_{F}$ related to meager-additive sets. We obtain a new characterization of additivity of meager ideal and answer some questions of Cardona. We also show that $\mathrm{non}(\mathcal{E}^{*})$, that is equal to the translation version of the covering number of the ideal $\mathcal{E}$, is close to the cardinal invariant related to the Laver property. This strengthens a result of Bartoszyński and Judah and a result of Elekes and Steprāns. Finally, we show that every $\mathcal{E}$-Luzin set is in $\mathcal{E}^{*}$.
