Structures Definable in O-Minimal Models

可在 O 最小模型中定义的结构

• 批准号: 9970551
• 负责人: Sergei Starchenko
• 金额: $ 7.11万
• 依托单位: University of Notre Dame
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-15 至 2002-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970551&HistoricalAwards=false
• 关键词: Structures; Definable; Minimal; Models

9970551Starchenko S. Starchenko will continue his research in the field ofmodel theory. He intends to study structures definable ino-minimal models, and he will also attempt to extend some recentresults about Pfaffian functions to o-minimal expansions of realclosed fields. One of the main goals of this research is developing a theoryof analytic functions over arbitrary algebraically closed fields(fields in which all polynomial equations in one variable havesolutions) analogous to the theory of complex analytic functions.S. Starchenko strongly believes that many classical theorems ofcomplex analysis can also be proved in the category of ``tameanalytic'' functions over such fields. Understanding which theoremsare available in this general context and which are not would shedlight on the classical theory itself; the new perspective would bemade to provide more insight into a highly developed and venerableclassical theory.***

小行星9970551 S. Starchenko将继续他在模型理论领域的研究。 他打算研究结构可定义的非最小模型，他也将试图扩大最近的一些结果Pfweian函数的O-最小扩展的realclosed领域。 本研究的主要目标之一是发展一种类似于复解析函数理论的任意代数闭域（其中所有的多项式方程都有解的域）上的解析函数理论. Starchenko坚信，复分析的许多经典定理也可以在此类域上的“tameanalytic”函数范畴中得到证明。 理解哪些定理在这个一般的背景下是可用的，哪些是不可用的，将有助于阐明经典理论本身;新的视角将为高度发展和受人尊敬的经典理论提供更多的见解。