The model theory of compact complex manifolds and other geometric strucutres

紧复流形及其他几何结构的模型理论

• 批准号: 312513-2010
• 负责人: Moosa, Rahim
• 金额: $ 1.75万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=526551
• 关键词: model; theory; compact; complex; manifolds

I am interested in the interaction between mathematical logic and geometry. Mathematical logic, to quote the opening lines of Shoenfield's book by that name, is the study of the type of reasoning done by mathematicians. Geometry is one of the core branches of mathematics itself; it is inspired by (and vastly generalises) the study of objects in three-dimensional space. Somewhat surprisingly, the methods of the meta-mathematical subject of logic have proved to be of substantial geometrical significance. Fundamentally, what logic brings to geometry is a "linguistic" intuition; the logician plays close attention to what can be expressed or defined in a given formal language. Associated to these formal expressions (syntax) are the objects they define (semantics), the "definable sets". Model theory, the particular branch of mathematical logic in which I specialise, could be described as the study of the geometrical properties of definable sets.

我对数学逻辑和几何形状之间的相互作用感兴趣。数学逻辑是用该名称引用Shoenfield的书的开头，是对数学家所做的推理类型的研究。几何是数学本身的核心分支之一。它的灵感来自（且广泛的）在三维空间中对物体的研究。有些令人惊讶的是，事实证明，逻辑的元数学主题的方法具有实质性的几何意义。从根本上讲，逻辑为几何带来的是“语言”的直觉。逻辑学家密切关注在给定的形式语言中可以表达或定义的内容。与这些形式表达式相关联（语法）是他们定义的对象（语义），即“可定义集”。模型理论是我专门研究的数学逻辑的特定分支，可以描述为对可定义集的几何特性的研究。