Model theory, algebra, and differential equations

该项目涉及将数理逻辑的一个分支--模型理论的思想应用于微分方程的分类。模型论研究结构和可定义集。从这个意义上讲，结构粗略地说是一个基本的集合或宇宙，以及集合中不同的n元组的一些不同的集合。数学的许多部分或对象可以作为结构来进行卓有成效的研究。另一方面，微分方程是描述变化率的方程，例如，一些量，它们隐藏在所有现代科学和许多现代技术的背后。该项目涉及将微分方程解的集合粗略地视为模型理论意义上的结构，并试图通过模型理论的工具来分类或理解此类方程。

The project concerns applying ideas from model theory, a branch of mathematical logic, to the classification of differential equations. Model theory studies structures and definable sets. A structure in this sense is roughly speaking an underlying set or universe together with some collection of distinguished sets of n-tuples from the set, for varying n. Many parts or objects of mathematics can be fruitfully studied as structures. Differential equations, on the other hand, are equations which describe the rate of change, for example, of some quantity, and they lie behind all of modern science and much of modern technology. The project involves roughly viewing the set of solutions of a differential equation as a structure in the sense of model theory, and attempting to classify or understand such equations via the tools of model theory.