Mathematical Sciences: RUI: Research in Model Theory

小行星9401723 这个项目的重点是与O-极小及其扩展有关的问题。 其中一些问题涉及到原型O-极小结构和结构的扩张，其域具有作为其序类型的真实的数。 其他问题有关o-极小的目的是发展的结构，集团可定义的o-最小的结构，尽可能在类比当地欧几里德集团。 其中的变种和扩展的o-极小要考虑的是弱o-极小和局部o-极小。 希望后者将提供一个合适的框架，发展一些模型理论的次解析集。 研究的另一个目标是开始发展一个通用的模型理论的有序结构，模式后的稳定性理论。 上述研究福尔斯属于数学分支逻辑中的模型论。 模型论试图处理熟悉的数学结构的属性，这些结构可以用形式化的数学语言（如谓词逻辑）来描述。 这个项目的重点是一个类，包括和行为非常像多项式和代数函数的基础上的真实的数字，在大一微积分研究，并用于描述许多现象。 在过去的五年里，模型理论在加深我们对逻辑以外的不同数学领域中感兴趣的熟悉数学系统的理解方面发挥了核心作用。 ***

9401723 Steinhorn This project focuses upon questions having to do with o-minimality and its extensions. Some of these questions relate to expansions of archetypal o-minimal structures and structures whose domain has as its order type that of the real numbers. Other problems concerning o-minimality are intended to develop the structure of groups definable in o-minimal structures as far as possible in analogy with locally Euclidean groups. Among the variants and extensions of o-minimality to be considered are weak o-minimality and local o-minimality. It is hoped that the latter will provide a suitable framework for developing some model theory for subanalytic sets. Another goal of the research is to begin to develop a general model theory for ordered structures, patterned after stability theory. The research described above falls under the heading of model theory within the branch of mathematics called logic. Model theory attempts to deal with the properties of familiar mathematical structures which can be described by a formal mathematical language such as predicate logic. The focus of this project is a class that includes and behaves very much like the polynomial and algebraic functions based on the real numbers that are studied in freshman calculus and are used to describe many phenomena. There has been much exciting progress during the past five years, in which model theory has played a central role in deepening our understanding of familiar mathematical systems of interest in diverse areas of mathematics outside of logic. ***