论文标题
传递性，lowness和NSOP中排名$ _1 $理论
Transitivity, lowness, and ranks in NSOP$_1$ theories
论文作者
论文摘要
我们在nsop $ _ {1} $理论的背景下发展了Kim-独立的理论理论，使存在公理。我们表明，在这种理论中，Kim-Intientence是一种传递性的，并且$ \ ind^{k} $ - Morley序列见证了Kim-Dividing。作为应用程序，我们表明，在存在的假设下，在低NSOP $ _ {1} $理论中，Shelah Strong类型和Lascar强类型是重合的，而且，我们介绍了NSOP $ _ {1} $理论的等级概念。
We develop the theory of Kim-independence in the context of NSOP$_{1}$ theories satsifying the existence axiom. We show that, in such theories, Kim-independence is transitive and that $\ind^{K}$-Morley sequences witness Kim-dividing. As applications, we show that, under the assumption of existence, in a low NSOP$_{1}$ theory, Shelah strong types and Lascar strong types coincide and, additionally, we introduce a notion of rank for NSOP$_{1}$ theories.
