Model Theory and Analysis

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

This project concerns the further development of Henson's logic for structures based on metric spaces and, especially, the continued application of this theory to problems in functional analysis and in the geometry of metric spaces. The syntax of this logic is restricted to the class of positive bounded formulas and the semantics of the logic uses an approximate satisfaction relation. Its potential role in analysis and geometry is parallel to the role of ordinary first order logic in the more algebraic aspects of mathematics. During the past 40 years or more, techniques from logic have not only clarified the foundations of mathematics, but they have contributed new tools for solving mathematical problems. These tools have been especially effective in those areas of mathematics that are close to algebra and number theory. In this project, C. Ward Henson aims to make those tools from logic equally effective in the areas of mathematics that are close to topology, geometry, and analysis.