Dp-minimality: basic facts and examples

Details Dp-minimality: basic facts and examples Dp-minimality: basic facts and examples

2009-10-16

arxiv.org/abs/0910.3189v2

Mathematics

Logic

19 pages; simplified proof for the p-adics

Scientific paper

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.

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