Combinatorial set theory

组合集合论

• 批准号: 1500790
• 负责人: James Cummings
• 金额: $ 17.69万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-06-01 至 2020-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1500790&HistoricalAwards=false
• 关键词: Combinatorial; set; theory

The main focus of the proposal is the investigation of several types of infinite structure, using a range of mathematical tools. A secondary focus is the investigation of problems about very large finite structures, using certain infinite "limit" structures. Some of the problems to be studied are "test questions" intended to stimulate the development of new idea and methods.The topics of the proposal are mostly concerned with large cardinals, ZFC combinatorics (particularly of singular cardinals) and forcing. They include forcing axioms for successors of singulars, various forms of the tree property, connections between compactness properties, PCF theory and universality numbers. The last section of the proposal is concerned with problems arising in Razborov's theory of flag algebras.

该提案的主要重点是使用一系列数学工具来研究几种类型的无限结构。第二个重点是使用某些无限“极限”结构来研究有关非常大的有限结构的问题。一些要研究的问题是“测试问题”，旨在刺激新思想和新方法的发展。提案的主题主要涉及大基数、ZFC 组合学（特别是奇异基数）和强迫。它们包括单数后继的强制公理、树属性的各种形式、紧性属性之间的联系、PCF 理论和普遍性数。该提案的最后一部分涉及拉兹博罗夫标志代数理论中出现的问题。