THE KIM–PILLAY THEOREM FOR ABSTRACT ELEMENTARY CATEGORIES
THE KIM–PILLAY THEOREM FOR ABSTRACT ELEMENTARY CATEGORIES
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抽象基本范畴的 Kim-Pillay 定理
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
M. Kamsma
中科院分区：
文献类型：
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作者：
M. Kamsma
摘要介绍了抽象初等范畴的框架，推广了某些一阶理论的模型范畴和模型子集范畴。任何AEC和任何紧凑的抽象理论(本-雅科夫提出的“猫”)构成AECat。特别是，我们在正逻辑和连续逻辑中找到了应用：正理论或连续理论的模型(子集)范畴是AECat。一阶逻辑的Kim-Pillay定理通过划分独立性所具有的性质来刻画简单理论。我们证明了具有合并性的AECats的Kim-Pillay定理的一个版本，推广了一阶版本和已有的正逻辑版本。
Abstract We introduce the framework of AECats (abstract elementary categories), generalizing 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 characterizes simple theories by the properties dividing independence has. We prove a version of the Kim–Pillay theorem for AECats with the amalgamation property, generalizing the first-order version and existing versions for positive logic.