Vector spaces with a dense-codense generic submodule

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2024-03-20 DOI:10.1016/j.apal.2024.103442

Alexander Berenstein , Christian d'Elbée , Evgueni Vassiliev

引用次数: 0

Abstract

We study expansions of a vector space V over a field $F$ , possibly with extra structure, with a generic submodule over a subring of $F$ . We construct a natural expansion by existentially defined functions so that the expansion in the extended language satisfies quantifier elimination. We show that this expansion preserves tame model theoretic properties such as stability, NIP, NTP₁, NTP₂ and NSOP₁. We also study induced independence relations in the expansion.

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具有密集编码通用子模的向量空间

我们研究了一个域上的向量空间（可能有额外的结构）的扩展，它有一个在.的子环上的通用子模组。我们用存在定义的函数构造了一个自然扩展，这样扩展语言中的扩展就满足了量词消元。我们证明，这种扩展保留了驯服的模型论性质，如稳定性、NIP、NTP、NTP 和 NSOP。我们还研究了扩展中的诱导独立关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.