简单结构的逼近
Approximation by simple structures
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中文总结 AI 辅助
本文修改Harrison-Shermoen的抽象框架，证明多个NSOP_1理论可由简单结构逼近，引入极限维数以恢复Kim-独立性，并给出不可逼近的实例。
中文摘要 AI 辅助
在Gwyneth Harrison-Shermoen的硕士论文中，她发展了一个抽象框架，用于逼近给定理论的结构，该框架推广了光滑可逼近结构的概念。当时，由于缺乏例子，该框架的适用范围尚不清楚。在本文中，我们将证明，在对框架进行轻微修改后，几个被充分理解的$\mathrm{NSOP}_1$理论实际上可以通过简单结构来逼近。我们讨论了从逼近中获得的极限结构的某些结构性质，并引入了极限维数的概念，作为在极限结构中恢复Kim-独立性的候选方案。我们还提供了一些不能用有限Morley秩结构逼近的结构的例子。
英文摘要
In her graduate thesis, Gwyneth Harrison-Shermoen developed an abstract framework for approximating structures of a given theory, which generalized the notion of smoothly approximable structures. At the time it was unclear how broadly the framework applied due to a lack of examples. In this paper we will show that with slight modification to the framework, several well-understood $\mathrm{NSOP}_1$ theories are in fact approximable by simple structures. We discuss certain structural properties of the limit structure that can be obtained from the approximation and introduce a notion of limit dimension as a candidate for recovering Kim-independence in the limit structure. We also provide some examples of structures that are not approximable by structures of finite Morley rank.
