On dp-minimal expansions of the integers

We show that if $\mathcal{Z}$ is a dp-minimal expansion of $(\mathbb{Z},+,0,1)$ that defines an infinite subset of $\mathbb{N}$, then $\mathcal{Z}$ is interdefinable with $ \left($\mathbb{Z}$,+,0,1, < \right) $\mathrm{.}Asacorollary,weshowthesamefordp-minimalexpansionsof$ \left($\mathbb{Z}$,+,0,1\right) $whichdonoteliminate$ \exists^{\infty} $.