Dp-minimality: basic facts and examples
Logic
2009-11-12 v2
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.
Keywords
Cite
@article{arxiv.0910.3189,
title = {Dp-minimality: basic facts and examples},
author = {Alfred Dolich and John Goodrick and David Lippel},
journal= {arXiv preprint arXiv:0910.3189},
year = {2009}
}
Comments
19 pages; simplified proof for the p-adics