The Journal of Symbolic Logic

Research Article

On dp-minimal ordered structures

Pierre Simon

Ens, Département de Mathématiques et Applications, 45, Rue d'Ulm, 75005 Paris, France and Département de Mathématiques, Bâtiment 425, Faculté des Sciences d'Orsay, Université Paris-Sud 11, F-91405 Orsay Cedex, France, E-mail: pierre.simon.05@normalesup.org

Abstract

We show basic facts about dp-minimal ordered structures. The main results are: dp-minimal groups are abelian-by-finite-exponent, in a divisible ordered dp-minimal group, any infinite set has nonempty interior, and any theory of pure tree is dp-minimal.

(Received September 29 2009)