Axiomatizations of Presburger Arithmetic With Predicates For Powers

Philipp Hieronymi, Michael Reitmeir, Xiaoduo Wang

We give a complete first-order axiomatization of the structure $(\mathbb{Z},+,({\ell }^{\mathbb{N}}{)}_{\ell \in L})$, where $L\subseteq {\mathbb{Z}}_{\ge 2}$ is a set of pairwise multipl…