Definable groups in d-minimal and related structures

d-最小及相关结构中的可定义群

• 批准号: 2743671
• 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: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2743671
• 关键词: Definable; groups; minimal; related; structures

This project lies at the nexus of model theory (mathematical logic) and group theory. The main objects of study are groups definable in various structures, which can be of topological/geometric nature, such as o-minimal structures and tame expansions of them, such as d-minimal structures.In the o-minimal setting, definable groups have been fairly understood with perhaps the most notable result being the solution of Pillay's conjecture, which draws an explicit connection between those groups and real Lie groups. Extensions of Pillay's conjecture in one of many possible expansions of o-minimal structures will be investigated in this project. Concrete examples include(a) the expansion of the real field by a predicate for the set of all integer powers of 2,(b) the expansion of the real ordered group by a predicate for the set of integer numbersThose settings have recently seen the development of model-theoretic tools, which will be used in this project.Potential applications include:- The solution of Compact Domination Conjecture in the above settings- Affine embeddings for definable groups in the above settings.

这个项目位于模型论（数理逻辑）和群论的联系。主要的研究对象是各种结构的可定义群，这些结构可以是拓扑/几何性质的，如o-极小结构和它们的驯服扩展，如d-极小结构。在o-极小的设置中，可定义群已经得到了相当的理解，也许最显着的结果是皮莱猜想的解决方案，它在这些群和真实的李群之间建立了明确的联系。本计画将探讨皮莱猜想在o-极小结构的许多可能扩展中的一个。具体的例子包括：（a）2的所有整数幂集合的谓词对真实的域的扩展，（B）整数集合的谓词对真实的有序群的扩展这些设置最近已经看到了模型理论工具的发展，将在本项目中使用。潜在的应用包括：-在上述设置中的紧凑支配猜想的解决方案-在上述设置中可定义群的仿射嵌入。