Mathematical Sciences: Topics in the Foundations of Mathematics

数学科学：数学基础主题

• 批准号: 8902765
• 负责人: Harvey Friedman
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-06-01 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902765&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Foundations; Mathematics

Friedman will continue research on a number of topics that he has initiated in recent years in collaboration with other researchers, including topics in definitional structure of mathematics, reverse mathematics, algorithmic procedures, general unified proof theory, model theory of real functions, Borel reducibility for classes of countable structures, and the transferability and provability of positive sentences. Friedman also intends to explore some additional topics mostly without collaboration, including research exposition, independence results, round-off structures, Hilbert's seventeenth problem, intuitionistic set theory, foundations of ultrafinitism, and foundations of experimental mathematics.

弗里德曼将继续研究许多主题， 近年来，他与其他 研究人员，包括定义结构的主题 数学，逆向数学，算法程序， 一般统一证明理论，真实的函数的模型理论， 可数结构类的Borel约化， 肯定句的可转移性和可证明性。 弗里德曼还打算主要探讨一些其他主题 如果没有合作，包括研究展览， 独立性结果，舍入结构，希尔伯特 第十七题，直觉集合论，基础 和实验数学的基础。