Model Theory and Analysis

这个项目强调与数学和计算机科学的其他领域有关的数理逻辑。沃德·汉森将使用逻辑学的方法来解决这些领域内的问题，并将逻辑作为形成新概念和提出新问题的基础。这个项目有以下主要方面：(A)进一步发展基于度量空间，特别是Banach空间的结构的Henson逻辑，并继续将这一理论应用于泛函分析中的问题；(B)从逻辑的角度研究指数和其他初等函数；以及(C)继续研究逻辑决策问题的计算复杂性，特别是那些出现在数学最核心领域的问题。在过去的40多年里，来自逻辑的技术不仅澄清了数学的基础，而且为解决数学问题贡献了新的工具。这些工具在那些接近代数和数论的数学领域尤其有效。在这个项目中，C.Ward Henson的目标是使那些来自逻辑的工具在接近拓扑学、几何学和分析的数学领域同样有效。

9970009Henson This project emphasizes mathematical logic in relation to otherareas of mathematics and computer science. C. Ward Henson will usemethods from logic to solve problems within these areas and will uselogic as a basis for formulating new concepts and posing new problemswithin them. This project has the following main aspects: (a) furtherdevelopment of Henson's logic for structures that are based on metricspaces, especially on Banach spaces, and continued application of thistheory to problems in functional analysis; (b) study of exponentiationand other elementary functions from the logical point of view; and (c)continued investigation of the computational complexity of logicaldecision problems, especially those arising in the most central areasof mathematics. During the past 40 years or more, techniques from logic have notonly clarified the foundations of mathematics, but they have contributednew tools for solving mathematical problems. These tools have beenespecially effective in those areas of mathematics that are close toalgebra and number theory. In this project, C. Ward Henson aims tomake those tools from logic equally effective in the areas of mathematicsthat are close to topology, geometry, and analysis.***