Mathematical Sciences: Logical Issues in Constructive Mathematics and Metamathematics of Algebra

数学科学：构造数学和代数元数学中的逻辑问题

• 批准号: 9007990
• 负责人: Philip Scowcroft
• 金额: --
• 依托单位: Wesleyan University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-08-01 至 1993-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9007990&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Logical; Issues; Constructive

Scowcroft's work, in mathematical logic, will center on constructive mathematics and the model-theory of p-adic fields. Having found an effective test for the constructive truth of propositions, in real algebra, of a bounded logical complexity, Scowcroft hopes to isolate a convenient set of axioms for these constructively true propositions. He also wants to learn whether first-order real algebra in Dana Scott's model for intuitionistic analysis is recursively undecidable. Scowcroft's new model for intuitionistic analysis may permit him to develop a new model for first-order real algebra, and recent work on subanalytic sets may allow him to extend his effective test for constructive truth to propositions involving certain transcendental functions. In the model-theory of p-adic fields, Scowcroft plans to study the properties of definable equivalence relations, the differences in expressive power between the first-order languages commonly used to describe a p-adic field, and the efficiency of quantifier-elimination procedures for Macintyre's first-order theory of the p-adics. These issues in the foundations of algebra bring modern mathematical logic to bear upon another related area. Syntheses of this sort have been the source of some of the most significant mathematics of our time.

斯考克罗夫特的工作，在数理逻辑，将集中在建设性数学和模型理论的p-adic领域。斯考克罗夫特在逻辑复杂性有限的真实的代数中找到了一个有效的命题构造性真理检验方法，他希望为这些构造性真理命题分离出一组方便的公理。他还想知道Dana Scott的直觉分析模型中的一阶真实的代数是否是递归不可判定的。斯考克罗夫特的新模型的直觉分析可能使他能够制定一个新的模式，一阶真实的代数，最近的工作，亚分析集可能使他延长他的有效测试建设性真理的命题涉及某些超越功能。在模型理论的p-adic领域，斯考克罗夫特计划研究的性质，可定义的等价关系，差异的表达能力之间的一阶语言通常用来描述一个p-adic领域，和效率的量词消除程序麦金太尔的一阶理论的p-adics。代数基础中的这些问题使现代数理逻辑对另一个相关领域产生影响。这类综合是我们这个时代一些最重要的数学的源泉。