Model Theory and Analysis

模型理论与分析

• 批准号: 0140677
• 负责人: C. Ward Henson
• 金额: $ 18.07万
• 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: 2002
• 资助国家: 美国
• 起止时间: 2002-06-15 至 2006-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0140677&HistoricalAwards=false
• 关键词: Model; Theory; Analysis

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.

这个项目涉及Henson的逻辑的进一步发展的结构为基础的度量空间，特别是，继续应用这一理论的问题，在泛函分析和几何的度量空间。 这种逻辑的语法被限制在一类正有界公式和语义的逻辑使用近似满足关系。 它在分析和几何中的潜在作用与普通一阶逻辑在数学代数方面的作用是平行的。在过去的40年或更长的时间里，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与拓扑学、几何学和分析密切相关的数学领域同样有效。