Model theory of analytic functions

解析函数模型论

• 批准号: 2881804
• 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: 2023
• 资助国家: 英国
• 起止时间: 2023 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2881804
• 关键词: Model; theory; analytic; functions

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: explore connections between surreal numbers, transseries and model theoretic classes of non-oscillating functions explore applications of Pila-Wilkie type results in tame expansions of the reals investigate o-minimality and model completeness for analytic functions built on definable reals in models of arithmetic

模型理论是数理逻辑的一个分支，它为根据数学结构的可定义集合的复杂性对其进行分类提供了强有力的工具。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。这个项目将研究与几个数学上感兴趣的解析函数相关的场的展开式的模型理论性质，但其行为尚未被当前的模型理论捕获，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：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探索Pila-Wilkie型结果在实数的驯服展开中的应用研究在算术模型中建立在可定义实数上的解析函数的o-极小性和模型完备性