Mathematical Sciences: Combinatorial Set Theory and Forcing

数学科学：组合集合论和强迫

• 批准号: 8704586
• 负责人: James Baumgartner
• 金额: $ 6.93万
• 依托单位: Dartmouth College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8704586&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Combinatorial; Set; Theory

Professor Baumgartner will work in combinatorial set theory, on problems of particular relevance to the theory of forcing and generic sets. Areas of research include combinatorial partition theorems, new notions of "freeness" of set-mappings associated with cardinality computations for closed unbounded subsets (involving also new varieties of box-principles), the structure theory of proper, omega-one-semi-proper and Axiom A partial orderings, generalizations of Martin's Axiom, and the cardinal sequences of superatomic Boolean algebras. These topics are in the foundations of set theory and their study will shed light on the most fundamental building blocks in mathematics.

鲍姆加特纳教授将研究组合集合论， 与强迫理论特别相关的问题， 类属集 研究领域包括组合划分 定理，新概念的“自由”的集合映射相关联 具有闭无界子集的基数计算 （涉及的还有新品种箱型原理），结构 真值论、ω-1-半真值论与公理A偏 排序，马丁公理的推广，和基数 超原子布尔代数序列 这些主题在 集合论的基础及其研究将阐明 数学中最基本的基石