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arXiv 2104.12989math.LOmath.CO
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单调NIP的特征化

Characterizations of monadic NIP

Samuel Braunfeld, Michael C. Laskowski

备注：
We include corrigenda to v2 in an appendix. The notion of endless indiscernible triviality is introduced and replaces indiscernible triviality throughout, in particular in Theorem 1.1. The claim regarding the failure of 4-wqo in Theorem 1.2 is withdrawn and remains unproved
发表信息：
Trans. Amer. Math. Soc. Ser. B 8 (2021), 948-970; Trans. Amer. Math. Soc. Ser. B 11 (2024), 1226-1232
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AI总结：

本文研究了单调NIP理论的特征化，通过类型有限可满足性条件和其他模型性质，证明了非结构结果。

摘要：

我们给出了若干关于何时一个完备的一阶理论T是单调NIP（即当通过任意一元谓词扩展T时不会出现独立性质）的特征化条件。核心特征化是一个关于类型有限可满足性的条件。其他特征化包括模型的分解、不可区分序列的行为以及禁止的配置。作为应用，我们证明了对于那些消除量词的hereditary有限子结构类，非结构结果。

英文摘要：

We give several characterizations of when a complete first-order theory $T$ is monadically NIP, i.e. when expansions of $T$ by arbitrary unary predicates do not have the independence property. The central characterization is a condition on finite satisfiability of types. Other characterizations include decompositions of models, the behavior of indiscernibles, and a forbidden configuration. As an application, we prove non-structure results for hereditary classes of finite substructures of non-monadically NIP models that eliminate quantifiers.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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