Model theory of valued fields as examples of theories with NIP

有价值领域的模型理论作为 NIP 理论的例子

• 批准号: 238875-2011
• 负责人: Haskell, Deirdre
• 金额: $ 0.8万
• 依托单位: McMaster University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2012
• 资助国家: 加拿大
• 起止时间: 2012-01-01 至 2013-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=508430
• 关键词: Model; theory; valued; fields; examples

Much of the power (and much of the difficulty) of mathematics comes from its abstractness. A mathematician will observe many different situations - the shape of petals in a flower, the diffusion of particles through a membrane, the flow of water in the confluence of rivers - and look for the features they have in common. By studying these features in an abstract way, we can understand what properties the different situations have which arise simply because they are examples of the abstract setting. By contrast, we can also understand what properties are special to each example.

数学的很多力量（和很多困难）来自于它的抽象性。数学家会观察许多不同的情况——花朵中花瓣的形状，粒子通过膜的扩散，河流汇合处的水流——并寻找它们的共同特征。通过以一种抽象的方式研究这些特征，我们可以理解不同的情况具有哪些属性，这些属性仅仅是因为它们是抽象设置的例子而产生的。通过对比，我们还可以了解每个示例的特殊属性。