论文标题
抽象基本类别的Kim-Pillay定理
The Kim-Pillay theorem for Abstract Elementary Categories
论文作者
论文摘要
我们介绍了AECAT（抽象基本类别）的框架，介绍了某些一阶理论的模型类别和模型子集的类别。任何AEC和任何紧凑的抽象理论（Ben-Yaacov引入的“ CAT”）形成了AECAT。特别是，我们发现在正逻辑和连续逻辑中的应用：阳性或连续理论的模型的（子集的类别）是AECAT。 一阶逻辑的Kim-Pillay定理通过分裂独立性具有的属性来表征简单的理论。我们证明了具有合并属性的AECATS的Kim-Pillay定理的版本，从而概括了一阶版本和现有版本的正面逻辑。
We introduce the framework of AECats (abstract elementary categories), generalising both the category of models of some first-order theory and the category of subsets of models. Any AEC and any compact abstract theory ("cat", as introduced by Ben-Yaacov) forms an AECat. In particular, we find applications in positive logic and continuous logic: the category of (subsets of) models of a positive or continuous theory is an AECat. The Kim-Pillay theorem for first-order logic characterises simple theories by the properties dividing independence has. We prove a version of the Kim-Pillay theorem for AECats with the amalgamation property, generalising the first-order version and existing versions for positive logic.
