Journal
NOTRE DAME JOURNAL OF FORMAL LOGIC
Volume 52, Issue 3, Pages 267-288Publisher
DUKE UNIV PRESS
DOI: 10.1215/00294527-1435456
Keywords
independence property; dp-minimal; weakly o-minimal; p-adic field
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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.
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