Measure reducibility of countable Borel equivalence relations
Measure reducibility of countable Borel equivalence relations
复制标题
测量可数 Borel 等价关系的可约性
DOI：
10.4007/annals.2017.185.2.1
复制
发表时间：
2017
影响因子：
4.9
通讯作者：
B. D. Miller
中科院分区：
文献类型：
--
作者：
Clinton T. Conley;B. D. Miller
我们证明，在测度可归约性下严格高于 $\mathbb{E}_0$ 的可数 Borel 等价关系的每个基都是不可数的，从而排除了 Glimm-Effros 二分法的自然概括。我们还使用比以前使用的参数简单得多的参数，将许多有关测度可归约性层次结构的抽象结构的已知结果推入其基础。
We show that every basis for the countable Borel equivalence relations strictly above $\mathbb{E}_0$ under measure reducibility is uncountable, thereby ruling out natural generalizations of the Glimm-Effros dichotomy. We also push many known results concerning the abstract structure of the measure reducibility hierarchy to its base, using arguments substantially simpler than those previously employed.