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.

该项目涉及描述性集理论的各个方面及其与分析的关系。 其中包括（i）研究鲍尔等效关系的结构，包括在一般描述性集中背景下，以及与诸如千古理论中产生的特定情况有关的研究，例如，例如，与群体轨道引起的等效关系。动作，以及（ii）谐波分析中的确定性和描述性分类问题和操作者代数理论。