类推导理论中的新稳定性转移

arXiv - MATH - Logic Pub Date : 2024-09-17 DOI:arxiv-2409.11248

Omar Leon Sanchez, Shezad Mohamed

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引用次数: 0

摘要

受微分域扩展的结构性质的启发，我们引入了这样一个概念：相对于另一个模型完备的理论 $T_0$ 而言，理论 $T$ 是类派生的。我们证明，当$T$包含一个模型同伴$T_+$时，有几个模型理论性质会从$T_0$转移到$T_+$。这些性质包括完备性、量词消除、稳定性、简单性和 NSOP$_1$。我们还观察到，除了微分场理论之外，类似推导理论的例子比比皆是。

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Neostability transfers in derivation-like theories

Motivated by structural properties of differential field extensions, we introduce the notion of a theory $T$ being derivation-like with respect to another model-complete theory $T_0$. We prove that when $T$ admits a model-companion $T_+$, then several model-theoretic properties transfer from $T_0$ to $T_+$. These properties include completeness, quantifier-elimination, stability, simplicity, and NSOP$_1$. We also observe that, aside from the theory of differential fields, examples of derivation-like theories are plentiful.

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arXiv - MATH - Logic

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