Mathematical Sciences: Descriptive Set Theory

数学科学：描述集合论

• 批准号: 9317509
• 负责人: Alexander Kechris
• 金额: $ 19.13万
• 依托单位: California Institute of Technology
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-04-15 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9317509&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Descriptive; Set; Theory

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. ***

9317509 Kechris这个项目集中在可定义的群体行动和等价关系的描述性集理论上。 特别是，它涉及波兰群体在波兰空间，其轨道等效关系，可数鲍勒等效关系的结构和分类，一般鲍雷尔等效关系的理论以及可确定的基数理论的结构和分类。 设定理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，可以防止悖论和矛盾。 另一方面，它在所有事物后面如此深刻，以至于有时允许在数学的广泛分离分支中衍生出非常一般的结果。 ***