Structures Definable in O-Minimal Models

[9970551] Starchenko S. Starchenko将继续他在模型理论领域的研究。他打算研究非极小模型中可定义的结构，并尝试将一些关于Pfaffian函数的最新结果推广到实闭域的非极小展开式上。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（所有一元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这些域上的“次解析”函数的范畴中得到证明。了解哪些定理在这种一般情况下可用，哪些不可用，将有助于揭示经典理论本身；这一新的观点将为一个高度发达和古老的古典理论提供更多的见解

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.***