论文标题
等效关系的相对较原性和鲍尔分区特性
Relative primeness and Borel partition properties for equivalence relations
论文作者
论文摘要
我们介绍了等效关系相对灵巧性的概念，加强了不可还原性的概念，并显示了许多标准基准等效关系的概念，即可能会增强相对灵量的不可质性。我们介绍了用于鲍尔等效关系的基本特性的几个类似物，包括标准空间上的Prime等价关系的概念和Borel分区属性。特别是，我们介绍了一个薄弱的紧凑性的概念，并表征了等价关系的分区属性$ {\ mathbb f} _2 $和$ {\ mathbb e} _1 $。我们还讨论了与原始性有关的二分法，并发现在相对较原性和鲍雷尔分区属性的框架内，可以查看许多与等价关系的可降低相关性有关的自然问题。
We introduce a notion of relative primeness for equivalence relations, strengthening the notion of non-reducibility, and show for many standard benchmark equivalence relations that non-reducibility may be strengthened to relative primeness. We introduce several analogues of cardinal properties for Borel equivalence relations, including the notion of a prime equivalence relation and Borel partition properties on quotient spaces. In particular, we introduce a notion of Borel weak compactness, and characterize partition properties for the equivalence relations ${\mathbb F}_2$ and ${\mathbb E}_1$. We also discuss dichotomies related to primeness, and see that many natural questions related to Borel reducibility of equivalence relations may be viewed in the framework of relative primeness and Borel partition properties.
