Mathematical Sciences: Model Theory and Analysis

数学科学：模型理论与分析

• 批准号: 9626628
• 负责人: C. Ward Henson
• 金额: $ 9.49万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-06-15 至 2000-02-29
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9626628&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Model; Theory; Analysis

DMS 9626628 C. Ward Henson C. Ward Henson seeks to use methods from logic to solve problems within other areas of mathematics and computer science, and to use logic as a basis for formulating new concepts and posing new problems within them. This project has the following main aspects: (a) the further development of Henson's logic for models based on Banach spaces (or, more generally, on metric spaces), and the continued application of this theory to problems of functional analysis; (b) the study of exponentiation and other elementary functions from the model-theoretic point of view; objectives of this study include determining the computational complexity of the first order theory of the real exponential field and axiomatizing the identities satisfied by such other elementary functions as the Gamma function; (c) continued investigation of the computational complexity of logical decision problems, especially those arising from the most central areas of mathematics. This project emphasizes the relations between symbolic logic and other areas of mathematics and computer science. During the past 40 years techniques from logic have not only clarified the foundations of mathematics, but have contributed new tools for solving mathematical problems. These tools have been particularly effective in those areas of mathematics close to algebra. This project concentrates on making those same logic tools equally effective in the areas of mathematics closer to topology and geometry.

DMS 9626628 C.沃德·亨森 C. Ward Henson试图使用逻辑方法来解决数学和计算机科学其他领域的问题，并使用逻辑作为制定新概念和提出新问题的基础。 该项目有以下几个主要方面：（a）进一步发展基于Banach空间模型的Henson逻辑（或者，更一般地说，度量空间），并继续应用这一理论的问题，功能分析;（B）研究指数和其他基本功能，从模型理论的观点;本文的目的是确定真实的指数场一阶理论的计算复杂性，并公理化Gamma函数等初等函数所满足的恒等式;（c）继续研究逻辑决策问题的计算复杂性，特别是那些产生于最核心的数学领域的问题。 这个项目强调了符号逻辑与数学和计算机科学的其他领域之间的关系。 在过去的40年里，逻辑技术不仅澄清了数学的基础，而且为解决数学问题提供了新的工具。 这些工具在接近代数的数学领域特别有效。 该项目致力于使这些相同的逻辑工具在更接近拓扑和几何的数学领域同样有效。