论文标题
衡量可计数鲍尔等效关系的降低性
Measure reducibility of countable Borel equivalence relations
论文作者
论文摘要
我们表明，在估计降低的$ \ mathbb {e} _0 $降低的情况下，可计数的等效关系的每个基础都是无法数量的，从而排除了Glimm-effros二分法的天然概括。我们还使用比以前使用的参数要简单得多，将有关衡量性层次结构的抽象结构的许多已知结果推向其基础。
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.
