Model theory of expansions of fields with analytic functions

模型论是数理逻辑的一个分支，它提供了一个强有力的工具，可以根据可定义集合的复杂性对数学结构进行分类。这在从真实的解析几何到数论的各个领域都产生了引人注目的应用。本项目将研究与数学中感兴趣的几个解析函数相关的场的展开的模型论性质，但其行为尚未被当前的模型论捕获，目的是获得具有新应用潜力的模型论控制。可能的方向包括：- 对跨指数函数的收缩群进行分类-证明复指数的适当约简的模型完备性结果-证明阿贝尔指数的指数代数闭包的情况-探索超实数、跨级数和非振荡函数的模型理论类之间的联系

Model theory, a branch of mathematical logic, provides powerful tools to classify mathematical structures according to the complexity of their definable sets. This has generated striking applications in various fields, from real analytic geometry to number theory.This project will study the model theoretic properties of expansions of fields related to several analytic functions of interest in mathematics, but whose behaviour is not yet captured by current model theory, with the aim of obtaining model theoretic control that has potential for new applications.Possible directions include:- classify contraction groups of transexponential functions- prove model-completeness results for suitable reducts of complex exponentiation- prove cases of exponential-algebraic closure for abelian exponentials- explore connections between surreal numbers, transseries and model theoretic classes of non-oscillating functions