Model Theory and Analysis

该项目涉及基于度量空间的Henson结构逻辑的进一步发展，特别是该理论在功能分析和度量空间几何问题中的继续应用。该逻辑的语法被限制为一类正有界公式，逻辑的语义使用近似满足关系。它在分析和几何中的潜在作用与普通一阶逻辑在数学中更多的代数方面的作用是平行的。在过去的40多年里，逻辑技术不仅阐明了数学的基础，而且为解决数学问题提供了新的工具。这些工具在那些接近代数和数论的数学领域特别有效。在这个项目中，C. Ward Henson的目标是使这些来自逻辑的工具在接近拓扑、几何和分析的数学领域同样有效。

This project concerns the further development of Henson's logicfor structures based on metric spaces and, especially, thecontinued application of this theory to problems in functionalanalysis and in the geometry of metric spaces. The syntax ofthis logic is restricted to the class of positive boundedformulas and the semantics of the logic uses an approximatesatisfaction relation. Its potential role in analysis andgeometry is parallel to the role of ordinary first order logic inthe more algebraic aspects of mathematics.During the past 40 years or more, techniques from logic have notonly clarified the foundations of mathematics, but they havecontributed new tools for solving mathematical problems. Thesetools have been especially effective in those areas ofmathematics that are close to algebra and number theory. In thisproject, C. Ward Henson aims to make those tools from logicequally effective in the areas of mathematics that are close totopology, geometry, and analysis.