Mathematical Sciences: Descriptive Set Theory

数学科学：描述集合论

• 批准号: 8914426
• 负责人: Howard Becker
• 金额: $ 4.02万
• 依托单位: University of South Carolina at Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-12-01 至 1992-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8914426&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Descriptive; Set; Theory

Descriptive set theory is the branch of mathematical logic concerned with definable sets of reals. The research involves several topics in descriptive set theory and in the relationship between descriptive set theory and other parts of mathematics, particularly analysis and topology. Some of these topics will be considered under various types of determinacy assumptions. An outline of the project follows. 1. Classical descriptive set theory and its connections with analysis and topology. 1.1 Classification of pointsets in the projective hierarchy. 1.2 Examples of descriptive set theoretic phenomena occurring in analysis and topology. 1.3 Descriptive set theory and functional analysis: Sequences in Banach spaces. 1.4 Descriptive set theory and topology: Paths, path- connectedness and simple connectedness. 2. Modern descriptive set theory and its connections with other parts of mathematical logic. 2.1 Set theory in the Cabal universe. 2.2 Descriptive set theory in Cabal universe. 2.3 Jump operators and inner model operators.

描述性集理论是与可定义的真实集集有关的数学逻辑的分支。 该研究涉及描述性集理论的几个主题以及描述性集理论与数学其他部分（尤其是分析和拓扑）之间的关系。 这些主题中的一些将在各种类型的决定性假设下考虑。 该项目的概述如下。 1。与分析和拓扑结合的经典描述集理论及其联系。 1.1投影层次结构中的积分分类。 1.2描述性设置理论现象的示例发生在分析和拓扑中。 1.3描述性集理论和功能分析：Banach空间中的序列。 1.4描述性集理论和拓扑：路径，路径连接性和简单连接性。 2。现代描述性集理论及其与数学逻辑其他部分的联系。 2.1集团宇宙中的理论。 2.2 Cabal Universe中的描述性理论。 2.3跳跃操作员和内部模型运算符。