Combinatorial set theory

组合集合论

• 批准号: 1101156
• 负责人: James Cummings
• 金额: $ 15.19万
• 依托单位: Carnegie-Mellon University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-06-01 至 2014-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1101156&HistoricalAwards=false
• 关键词: Combinatorial; set; theory

Cummings proposes a program of research in combinatorial set theory.Infinite graphs, trees and orderings are the main objects of research in this program. The proposed research uses a wide range of techniques including forcing, PCF theory and inner model theory. The immediate goal of Cummings' research program is to get a better understanding of certain infinite mathematical structures. Problems about these structures arise in many areas of mathematics including algebra, analysis, topology and (perhaps surprisingly) the study of finite structures. The long term goal is to forge new tools for the construction and analysis of infinite structures, which should then find broader application.

Cummings提出了一个组合集合论的研究纲领，该纲领主要研究无限图、树和序。拟议的研究使用了广泛的技术，包括强迫，PCF理论和内模理论。 卡明斯研究计划的直接目标是更好地理解某些无限数学结构。关于这些结构的问题出现在数学的许多领域，包括代数，分析，拓扑学和（也许令人惊讶的）有限结构的研究。 长期目标是为无限结构的构建和分析打造新的工具，然后应该找到更广泛的应用。