Expansion of Presburger arithmetic with the exchange property

Abstract

Let $G$ be a model of Presburger arithmetic. Let $\mathcal{L}$ be an expansion of the language of Presburger ${\mathcal{L}}_{Pres}$. In this paper we prove that the $\mathcal{L}$-theory of $G$ is ${\mathcal{L}}_{Pres}$-minimal iff it has the exchange property and any bounded definable set has a maximum.

10 pages