A Family of dp-Minimal Expansions of (Z;+)

Abstract

We consider structures of the form $(\mathbb{Z};+,C)$, where C is an additive cyclic order on $(\mathbb{Z};+)$. We show that such structures are dp-minimal and in this way produce a continuum-size family of dp-minimal expansions of $(\mathbb{Z};+)$ such that no two members of the family define the same subsets of $\mathbb{Z}$.