Applications of Set Theory to Topology and Topology to Model Theory

集合论在拓扑中的应用以及拓扑在模型论中的应用

• 批准号: RGPIN-2016-06319
• 负责人: Tall, Franklin
• 金额: $ 1.31万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635497
• 关键词: Applications; Set; Theory; Topology; Model

This research applies one field of mathematics (Set Theory) to another (Topology), as well as the second to a third (Model Theory). Set Theory is the study of the fundamental building blocks (sets) of the mathematical universe; Topology is the study of abstractions of geometric properties of space; Model Theory is the study of languages and how languages relate to the structures they describe. By definition, Pure Mathematics, such as these fields, does not concern itself with real-world applications. Nonetheless, time after time, such basic research has led to important technological advances, such as the development of the computer, which were not foreseen by the early pioneers in such research. Therefore, wise governments fund basic research.

本研究将数学的一个领域（集合论）应用于另一个领域（拓扑学），并将第二个领域应用于第三个领域（模型论）。集合论是对数学宇宙的基本构建块（集合）的研究；拓扑学是对空间几何性质的抽象研究；模型理论是一门研究语言以及语言如何与它们所描述的结构相联系的学科。根据定义，纯数学，比如这些领域，并不关心现实世界的应用。然而，一次又一次，这样的基础研究导致了重要的技术进步，比如计算机的发展，这是早期研究先驱们没有预见到的。因此，明智的政府会资助基础研究。