Mathematical Sciences: Combinatorial Set Theory, Forcing andPriority Arguments

数学科学：组合集合论、强迫和优先级论证

• 批准号: 8906946
• 负责人: James Baumgartner
• 金额: $ 6.65万
• 依托单位: Dartmouth College
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1992-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8906946&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Combinatorial; Set; Theory

Baumgartner will work on problems in the theory of forcing and on combinatorial set theory, in particular on combinatorial problems that seem to raise fundamental questions about forcing. Forcing is a powerful method for examining the extremes of set theoretic behavior permitted by given axioms of set theory. One uses it to construct models of set theory obeying the axioms, the object being to show that some additional property does not follow from the axioms. If one can show that neither a property nor its opposite follows from the axioms, one has found an independence proof for that property. These are highly prized as illuminating the foundations of set theory and thereby of all mathematics.

Baumgartner将在强迫和组合理论理论中处理问题，尤其是在似乎引发强迫基本问题的组合问题上。 强迫是一种有力的方法，用于检查给定的设定理论公理所允许的设置理论行为的极端。 一个人用它来构建遵守公理的设置理论模型，其目的是表明某些其他属性并不遵循公理。 如果一个人都不能从公理上遵循财产和相反的情况，那么人们已经找到了该属性的独立证明。 这些被高度珍贵，以照明设定理论的基础以及所有数学的基础。