Dp-Minimality: Basic Facts and Examples

Notre Dame Journal of Formal Logic 52 (3):267-288 (2011)
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Abstract

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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Citations of this work

Theories without the tree property of the second kind.Artem Chernikov - 2014 - Annals of Pure and Applied Logic 165 (2):695-723.
On non-compact p-adic definable groups.Will Johnson & Ningyuan Yao - 2022 - Journal of Symbolic Logic 87 (1):188-213.
Distal and non-distal NIP theories.Pierre Simon - 2013 - Annals of Pure and Applied Logic 164 (3):294-318.
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