On the Decidability of Presburger Arithmetic Expanded with Powers
Toghrul Karimov, Florian Luca, Joris Nieuwveld, Joël Ouaknine, James Worrell · arXiv (Cornell University) · 2024
We prove that for any integers $α, β> 1$, the existential fragment of the first-order theory of the structure $\langle \mathbb{Z}; 0,1, 1$ would lead to mathematical breakthroughs regarding base-$α$ and base-$β$ expansions of certain transcendental numbers.