Dp-minimal expansions of discrete ordered abelian groups

Abstract

If \(\mathscr{Z}\) is a dp-minimal expansion of a discrete ordered abelian group \((Z,<,+)\) and \(\mathscr{Z}\) does not admit a nontrivial definable convex subgroup then \(\mathscr{Z}\) is interdefinable with \((Z,<,+)\) and \((Z,<,+)\) is elementarily equivalent to \((\mathbb{Z},<,+)\).