On the Decidability of Presburger Arithmetic Expanded with Powers

Toghrul Karimov, Florian Luca, Joris Nieuwveld +2

We prove that for any integers $\hat{I}\pm ,{\hat{I}}^2>1$, the existential fragment of the first-order theory of the structure $\langle \mathbb{Z}; 0,1,<, +, α^{\mathbb{N}}, β^{\mathbb{N}}\rang…