Mathematical Sciences: Descriptive Set Theory

9317509 Kechris这个项目专注于可定义的群动作和等价关系的描述性集合理论。特别讨论了Polish群在Polish空间上的Borel作用、它们的轨道等价关系、可数Borel等价关系的结构和分类、广义Borel等价关系理论和可定义基数理论。集合论是所有数学的基础。一方面，它提供了一种精神卫生，防止自相矛盾和矛盾。另一方面，它是如此深刻地隐藏在一切事物的背后，以至于有时它允许在广泛分离的数学分支中应用来推导非常一般的结果。***

9317509 Kechris This project concentrates on the descriptive set theory of definable group actions and equivalence relations. In particular, it deals with Borel actions of Polish groups on Polish spaces, their orbit equivalence relations, the structure and classification of countable Borel equivalence relations, the theory of general Borel equivalence relations, and definable cardinality theory. Set theory lies at the foundation of all mathematics. On the one hand, it provides a form of intellectual hygiene, protecting against paradox and contradiction. On the other hand, it lies so deeply behind everything that it sometimes permits derivation of very general results with application in widely separated branches of mathematics. ***