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.Comment: 19 pages; simplified proof for the p-adic
