A new dp-minimal expansion of the integers

Eran Alouf, Christian d'Elbée

We consider the structure $(\mathbb{Z},+,0,{|}_{p_1},\dots ,{|}_{p_n})$, where $x{|}_{p}y$ means $v_p(x)\le v_p(y)$ and $v_p$ is the $p$-adic valuation. We prove that its theory…