DP-极小性：基本事实和例子
Dp-minimality: basic facts and examples
摘要：
我们研究了dp-极小性的概念，首先提供了几个基本事实，建立了几个等价的定义，并比较了dp-极小性与其他极小性概念。本文的其余部分是专门的例子。我们建立通过一个简单的证明，任何弱o-极小理论是dp-极小的，然后给出一个例子，弱o-极小群不是通过添加外可定义集的迹。其次，我们给出了一个可分有序阿贝尔群的例子，它是dp-极小而不是弱o-极小的。最后证明了p-adic数域是dp-极小的。
英文摘要：
We study the notion of dp-minimality, beginning by providing several essential facts, establishing several equivalent definitions, and comparing dp-minimality to other minimality notions. The rest of the paper is dedicated to examples. We establish via a simple proof that any weakly o-minimal theory is dp-minimal and then give an example of a weakly o-minimal group not obtained by adding traces of externally definable sets. Next we give an example of a divisible ordered Abelian group which is dp-minimal and not weakly o-minimal. Finally we establish that the field of p-adic numbers is dp-minimal.
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。
