Model theory of expansions of fields with analytic functions

具有解析函数的域展开模型论

• 批准号: 2273512
• 金额: --
• 依托单位: University of Leeds
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2273512
• 关键词: Model; theory; expansions; fields; analytic

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

模型论是数学逻辑的一个分支，它提供了根据可定义集的复杂性对数学结构进行分类的强大工具。这在各个领域产生了惊人的应用，从真正的解析几何到数论。该项目将研究与数学中几个分析函数相关的领域展开的模型理论性质，但其行为尚未被当前模型理论捕获，目的是获得具有新应用潜力的模型理论控制。可能的方向包括：-分类转幂函数的收缩群-证明复幂的合适约化的模型完备性结果-证明阿贝尔指数的指数代数闭包的情况-探索超现实数、转级数和非振荡函数的模型理论类之间的联系