论文标题
矢量空间，具有致密的通用子模块
Vector spaces with a dense-codense generic submodule
论文作者
论文摘要
我们研究了矢量空间$ v $的扩展，这可能是$ \ mathbb f $，可能具有额外的结构，并在$ \ mathbb f $的子弹子上带有通用的子模块。我们通过存在定义的函数构建自然扩展，以使扩展语言的扩展满足消除量子的消除。我们表明，这种扩展可以保留驯服模型理论属性，例如稳定性，NIP，NTP $ _1 $，NTP $ _2 $和NSOP $ _1 $。我们还研究了扩张中诱导的独立关系。
We study expansions of a vector space $V$ over a field $\mathbb F$, possibly with extra structure, with a generic submodule over a subring of $\mathbb F$. 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, NTP$_1$, NTP$_2$ and NSOP$_1$. We also study induced independence relations in the expansion.
