Open Access
2011 Dp-Minimality: Basic Facts and Examples
Alfred Dolich, John Goodrick, David Lippel
Notre Dame J. Formal Logic 52(3): 267-288 (2011). DOI: 10.1215/00294527-1435456


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.


Download Citation

Alfred Dolich. John Goodrick. David Lippel. "Dp-Minimality: Basic Facts and Examples." Notre Dame J. Formal Logic 52 (3) 267 - 288, 2011.


Published: 2011
First available in Project Euclid: 28 July 2011

zbMATH: 1258.03036
MathSciNet: MR2822489
Digital Object Identifier: 10.1215/00294527-1435456

Primary: 03C45
Secondary: 03C64

Keywords: dp-minimal , independence property , p-adic field , weakly o-minimal

Rights: Copyright © 2011 University of Notre Dame

Vol.52 • No. 3 • 2011
Back to Top