Borel Equivalence Relations
Borel Equivalence Relations
复制标题
Borel 等价关系
DOI：
--
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
G. Hjorth
中科院分区：
文献类型：
--
作者：
G. Hjorth
本文调查了在 Borel 约简性排序下 Borel 等价关系快速发展的领域。尽管该领域现在被认为是描述性集合论的一部分，但它的起源可以追溯到完全逻辑之外的领域。事实上，本次调查从西尔弗关于协同分析等价关系的等价类数量的定理和具有里程碑意义的 Harrington-Kechris-Louveau 二分定理开始，但也仔细概述了该主题的一些史前史，追溯到遍历理论、动力学、群论和泛函分析的根源。
This article surveys the rapidly evolving area of Borel equivalence relations under the ordering of Borel reducibility. Although the field is now considered part of descriptive set theory, it traces its origins back to areas entirely outside logic. In fact this survey starts with Silver’s theorem on the number of equivalence classes of a co-analytic equivalence relation and the landmark Harrington-Kechris-Louveau dichotomy theorem, but also takes care to sketch some of the prehistory of the subject, going back to the roots in ergodic theory, dynamics, group theory, and functional analysis.