Model Theory and Analysis

9970009亨森 这个项目强调数学逻辑与数学和计算机科学的其他领域的关系。 C. Ward Henson将使用逻辑方法来解决这些领域内的问题，并将使用逻辑作为制定新概念和提出新问题的基础。 本项目的主要内容如下：（a）进一步发展基于度量空间，特别是Banach空间的Henson结构逻辑，并继续将该理论应用于泛函分析问题：（B）从逻辑观点研究指数和其它初等函数;以及（c）继续研究逻辑决策问题的计算复杂性，特别是那些出现在最核心的数学领域的问题。 在过去的40年或更长的时间里，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。 这些工具在那些与代数和数论密切相关的数学领域特别有效。 在本项目中，C. Ward Henson的目标是使这些来自逻辑的工具在接近拓扑学、几何学和分析的几何学领域同样有效。

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.***