Submission date: 19 October 2009.

Abstract:

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.

Mathematics Subject Classification: 03C68, 03C64

Keywords and phrases: dp-minimality, weak o-minimality, p-adic numbers

Full text arXiv: pdf, ps.