当前位置: X-MOL 学术J. Math. Log. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
A generalization of the 𝔾0 dichotomy and a strengthening of the 𝔼0ℕ dichotomy
Journal of Mathematical Logic ( IF 0.9 ) Pub Date : 2021-07-05 , DOI: 10.1142/s0219061321500288
Benjamin D. Miller 1
Affiliation  

We generalize the 𝔾0 dichotomy to doubly-indexed sequences of analytic digraphs. Under a mild definability assumption, we use this generalization to characterize the family of Borel actions of tsi Polish groups on Polish spaces that can be decomposed into countably-many Borel actions admitting complete Borel sets that are lacunary with respect to an open neighborhood of the identity. We also show that if the group in question is non-archimedean, then the inexistence of such a decomposition yields a special kind of continuous embedding of 𝔼0 into the corresponding orbit equivalence relation.

中文翻译:

𝔾0二分法的推广和𝔼0ℕ二分法的加强

我们概括𝔾0分析有向图的双索引序列的二分法。在一个温和的可定义性假设下,我们使用这种概括来刻画 tsi 波兰群在波兰空间上的 Borel 动作族,这些动作可以分解为可数的多个 Borel 动作,它们承认完整的 Borel 集相对于恒等式的开放邻域是空缺的. 我们还表明,如果所讨论的群是非阿基米德群,那么这种分解的不存在会产生一种特殊的连续嵌入𝔼0成相应的轨道等价关系。
更新日期:2021-07-05
down
wechat
bug