Bi-interpretability with $\mathbb{Z}$ and models of the complete elementary theories of ${\text{SL}}_n(\mathcal{O})$, ${\text{T}}_n(\mathcal{O})$ and ${\text{GL}}_n(\mathcal{O})$, $n\ge 3$

Mahmood Sohrabi, Alexei G. Myasnikov

Let $\mathcal{O}$ be the ring of integers of a number field, and let $n\ge 3$. This paper studies bi-interpretability of the ring of integers $\mathbb{Z}$ with the special linear…