Dp-Minimality: Basic Facts and Examples
Dp-Minimality: Basic Facts and Examples
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Dp-极简：基本事实和示例
DOI：
10.1215/00294527-1435456
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
David Lippel
中科院分区：
文献类型：
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作者：
Alfred Dolich;John Goodrick;David Lippel
我们研究极小性的概念，从提供几个基本事实开始，建立几个等效的定义，并将极小性与其他极小性概念进行比较。论文的其余部分都是用例子来说明的。通过一个简单的证明，证明了任何弱o-极小理论都是dp-极小的，并给出了一个不是通过添加外部可定义集的迹得到的弱o-极小群的例子。然后给出一个可除有序阿贝尔群的例子，它是dp极小而不是弱o极小。最后证明了p进数域是dp极小域。
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.