The additive groups of $\mathbb{Z}$ and $\mathbb{Q}$ with predicates for being square-free

Neer Bhardwaj, Minh Chieu Tran

We consider the four structures $(\mathbb{Z};{\mathrm{Sqf}}^{\mathbb{Z}})$, $(\mathbb{Z};<,{\mathrm{Sqf}}^{\mathbb{Z}})$, $(\mathbb{Q};{\mathrm{Sqf}}^{\mathbb{Q}})$, and $(\mathbb{Q}; <, \…