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.

描述集合论是数理逻辑的一个分支，研究实数的可定义集合。研究涉及到描述集合论的几个主题，以及描述集合论与数学的其他部分，特别是分析和拓扑之间的关系。其中一些主题将在不同类型的确定性假设下考虑。下面是该项目的概要。1. 经典描述集合论及其与分析和拓扑学的联系。1.1投影层次中点集的分类。1.2分析和拓扑学中出现的描述性集合论现象的例子。1.3描述集论与泛函分析：Banach空间中的序列。1.4描述集理论与拓扑学：路径、路径连通性和简单连通性。2. 现代描述性集合论及其与数理逻辑其他部分的联系。2.1阴谋集团宇宙中的集合理论。2.2《阴谋论》宇宙中的描述性集合理论。2.3跳转操作符和内部模型操作符。