On the Decidability of Presburger Arithmetic Expanded with Powers

Toghrul Karimov, Florian Luca, Joris Nieuwveld +2

We prove that for any integers $\alpha ,\beta >1$, the existential fragment of the first-order theory of the structure $⟨\mathbb{Z};0,1,<,+,{\alpha }^{\mathbb{N}},{\beta }^{\mathbb{N}}⟩$…