Mathematical Sciences: Set Theory

数学科学：集合论

• 批准号: 9103042
• 负责人: William Woodin
• 金额: $ 16.49万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-05-15 至 1994-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103042&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Set; Theory

Set theory underlies all of mathematics. The two main avenues to laying the foundations of set theory rely either on axioms postulating large cardinal numbers or on various axioms about the determinacy of so-called set theoretic games. Woodin will investigate the relationship between large cardinals and determinacy, descriptive set theory in the context of determinacy, and the possibilities for the definability of the well-ordering of the reals in the presence of very large cardinals. He also intends to investigate the global structure of the Turing degrees and of more general degree structures. The basic question concerns rigidity.

集合论是所有数学的基础。 两条主要途径 奠定集合论的基础， 假设大基数或各种公理 所谓的集合论游戏的确定性。 伍丁将调查大型 基数和确定性，描述性集合论的背景下， 第二章论人与人之间的关系 在有非常大的基数的情况下实数的良序。 他还打算研究图灵机的全球结构 学位和更一般的学位结构。 的根本问题 关于刚性。