Combinatorial Set Theory

组合集合论

• 批准号: 0070549
• 负责人: James Cummings
• 金额: $ 7.66万
• 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: 2000
• 资助国家: 美国
• 起止时间: 2000-05-01 至 2003-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070549&HistoricalAwards=false
• 关键词: Combinatorial; Set; Theory

The investigator proposes a program of research in axiomatic set theory. The program involves looking at a number of different questions, all of which involve combinatorial set theory and are related to large cardinals and forcing; among the areas to be studied are mutual stationarity, identity crises for large cardinals, and combinatorial principles. The techniques to be used include Radin forcing, iterated forcing and PCF theory. Combinatorial set theory is a discipline whose goal is to take familiar ideas about finite sets (such as counting, ordering and permuting) and extend them to the context of infinite sets. The theory is highly developed and has found applications in several mathematical areas where infinite sets are used, including topology and analysis. Progress on the problems which are proposed by the investigator should increase our understanding of infinite sets, and help forge tools which will be useful to set theorists and workers in other areas.

研究人员提出了一个公理集合论的研究计划。该计划涉及研究许多不同的问题，所有这些问题都涉及组合集合论，并且与大基数和强迫有关；要研究的领域包括相互平稳性、大主教的身份危机和组合原则。所使用的技术包括 Radin 强迫、迭代强迫和 PCF 理论。 组合集合论是一门学科，其目标是将有限集合的常见概念（例如计数、排序和排列）扩展到无限集合的环境中。 该理论已经高度发展，并已在使用无限集的多个数学领域得到应用，包括拓扑和分析。 研究者提出的问题的进展应该会增加我们对无限集的理解，并有助于打造对其他领域的集合理论家和工作者有用的工具。