Mathematical Sciences: Descriptive Set Theory

数学科学：描述集合论

• 批准号: 9020153
• 负责人: Alexander Kechris
• 金额: $ 20.94万
• 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: 1991
• 资助国家: 美国
• 起止时间: 1991-02-01 至 1994-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9020153&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Descriptive; Set; Theory

This project deals with aspects of descriptive set theory and its relationship with analysis. These include (i) the study of the structure of Borel equivalence relations, both in a general descriptive set theoretic context, as well as in connection with specific situations arising in ergodic theory, as, for example, with equivalence relations induced by orbits of group actions, and (ii) definability and descriptive classification problems in harmonic analysis and the theory of operator algebras.

这个项目涉及描述集合论的各个方面及其与分析的关系。这些包括：(1)研究Borel等价关系的结构，既在一般描述集论的背景下，也结合遍历理论中出现的具体情况，例如，与由群行动的轨道引起的等价关系，和(Ii)调和分析和算子代数理论中的可定义性和描述性分类问题。