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.

鲍姆加特纳将研究强迫理论和组合集理论中的问题，特别是那些似乎提出了关于强迫的基本问题的组合问题。强迫是检验给定的集合论公理所允许的集合论行为的极值的一种强有力的方法。一个人用它来构造遵从公理的集合理论模型，目的是证明一些附加的性质不能从公理中推导出来。如果一个人能证明一个性质和它的对立面都不能从公理中推导出来，那么他就找到了该性质的独立证明。这些理论被高度评价为阐明了集合论的基础，从而阐明了所有数学的基础。