标题： 一个贝尔空间中的理想动物园 显示英文标题

标题： An Ideal Zoo in the Baire Space

摘要： 在本文中，我们研究了几种在康托空间上定义的著名$\sigma$-理想和族在贝尔空间中的翻译，使用它们的组合特征。 这些包括零测集的理想、小集、由闭零测集生成的理想以及稀疏集，从而得到它们在贝尔空间中的“假”类似物。 我们还通过从$\omega^\omega$的函数对与零测集相关的族进行参数化。 研究了这些族的一些结构性质和相互关系，包括它们是否形成理想、是否存在大的链和反链、正交性、$\kappa$-链条件以及某些基数不变量的确定。 显示英文摘要

摘要： In this paper, we study the translations into the Baire space of several well-known $\sigma$-ideals and families originally defined on the Cantor space, using their combinatorial characterizations. These include the ideals of null sets, small sets, those generated by closed measure-zero sets, and the meager sets, leading to their "fake" analogues in the Baire space. We also parametrize families related to null sets by functions from $\omega^\omega$. Several structural properties and relations between these families are investigated, including whether they form ideals, the existence of large chains and antichains, orthogonality, the $\kappa$-chain condition, and the determination of certain cardinal invariants.