NSOP $_1$ -LIKE INDEPENDENCE IN AECATS
NSOP
$_1$
-LIKE INDEPENDENCE IN AECATS
复制标题
NSOP $_1$ - 就像 AECATS 中的独立性
DOI：
--
复制
发表时间：
2021
期刊：
影响因子：
--
通讯作者：
M. Kamsma
中科院分区：
文献类型：
--
作者：
M. Kamsma
抽象类稳定，简单，NSOP
$_1$
在一阶理论的稳定性层次中，可以通过存在一定的独立关系来表征。对于它们中的每一个都有一个规范性定理：最多可以有一个好的独立关系。稳定和简单的一阶理论的独立性必须来自分叉和分裂（然后重合），对于NSOP，
$_1$
理论上它一定来自于金的分裂。我们概括这项工作的框架抽象基本范畴（AECats）的合并财产。这是一种可接近的范畴，它概括了某些理论的模型（子集）的范畴。我们证明了稳定，简单和NSOP的规范性定理
$_1$
- 像独立关系。稳定和简单的情况之前已经在稍微不同的设置中完成了，但是我们在这里也提供了它们，以便我们可以恢复原始稳定性层次的一部分。我们还提供了抽象的定义，这些独立的关系，我们称之为isi划分，isi分叉，和长期金划分。
Abstract The classes stable, simple, and NSOP
$_1$
in the stability hierarchy for first-order theories can be characterised by the existence of a certain independence relation. For each of them there is a canonicity theorem: there can be at most one nice independence relation. Independence in stable and simple first-order theories must come from forking and dividing (which then coincide), and for NSOP
$_1$
theories it must come from Kim-dividing. We generalise this work to the framework of Abstract Elementary Categories (AECats) with the amalgamation property. These are a certain kind of accessible category generalising the category of (subsets of) models of some theory. We prove canonicity theorems for stable, simple, and NSOP
$_1$
-like independence relations. The stable and simple cases have been done before in slightly different setups, but we provide them here as well so that we can recover part of the original stability hierarchy. We also provide abstract definitions for each of these independence relations as what we call isi-dividing, isi-forking, and long Kim-dividing.