We explore Shelah's model‐theoretic dividing line methodology. In particular, we discuss how problems in model theory motivated new techniques in model theory, for example classifying theories by their potential (consistently with Zermelo–Fraenkel set theory with the axiom of choice (ZFC)) spectrum of cardinals in which there is a universal model. Two other examples are the study (with Malliaris) of the Keisler order leading to a new ZFC result on cardinal invariants and attempts to clarify the “main gap” by reducing the dependence of certain versions on (highly independent) cardinal arithmetic.

中文翻译：

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分界线方法论：模型理论激励集理论

我们将探讨Shelah的模型理论分界线方法。特别是，我们讨论了模型理论中的问题是如何激发模型理论中的新技术的，例如根据具有潜在普遍性的红衣主教根据其潜力（与Zermelo–Fraenkel集理论和选择公理一致）对理论进行分类。模型。另外两个例子是对Keisler阶的研究（与Malliaris一起），该研究导致了基数不变性的新ZFC结果，并试图通过减少某些版本对（高度独立）基数算术的依赖性来澄清“主要差距”。