Dp-Minimality: Basic Facts and Examples

被引：37

作者：

Dolich, Alfred ^{[1
]}

Goodrick, John ^{[2
,3
]}

Lippel, David ^{[4
]}

机构：

[1] E Stroudsburg Univ, Dept Math, E Stroudsburg, PA 18301 USA

[2] Univ Los Andes, Dept Matemat, Bogota 111711, Colombia

[3] Univ Maryland, Dept Math, College Pk, MD 20742 USA

[4] Haverford Coll, Dept Math, Haverford, PA 19041 USA

来源：

NOTRE DAME JOURNAL OF FORMAL LOGIC | 2011年 / 52卷 / 03期

关键词：

independence property; dp-minimal; weakly o-minimal; p-adic field;

D O I：

10.1215/00294527-1435456

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the notion of dp-minimality, beginning by providing several essential facts about dp-minimality, establishing several equivalent definitions for dp-minimality, and comparing dp-minimality to other minimality notions. The majority of 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.

引用

页码：267 / 288

页数：22