Mathematical Sciences: Descriptive Set Theory

小行星9317509 这个项目集中在可定义的群体行动和等价关系的描述集合论。 特别是，它涉及波兰空间上的波兰群的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，一般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，它提供了一种智力卫生的形式，防止悖论和矛盾。 另一方面，它深深地隐藏在一切事物的背后，以至于它有时允许导出非常普遍的结果，并应用于广泛分离的数学分支。 ***

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. ***