论文标题
带有$ \ Mathbb {z} $的BI-Interpretable和$ \ text {sl} _n的完整基本理论的模型（\ Mathcal {o}）$，$ \ text {t} _n（\ Mathcal {o {o}）
Bi-interpretability with $\mathbb{Z}$ and models of the complete elementary theories of $\text{SL}_n(\mathcal{O})$, $\text{T}_n(\mathcal{O})$ and $\text{GL}_n(\mathcal{O})$, $n\geq 3$
论文作者
论文摘要
令$ \ mathcal {o} $为数字字段的整数环，让$ n \ geq 3 $。本文通过特殊线性组$ \ text {sl} _n（\ Mathcal {o}）$研究了整数环$ \ mathbb {z} $的双解释性，这$ \ MATHCAL {O} $，$ \ text {t} _n（\ Mathcal {o}）$。对于这些组中的每一个，我们提供了其完整基本理论的任意模型的完整表征。
Let $\mathcal{O}$ be the ring of integers of a number field, and let $n\geq 3$. This paper studies bi-interpretability of the ring of integers $\mathbb{Z}$ with the special linear group $\text{SL}_n(\mathcal{O})$, the general linear group $\text{GL}_n(\mathcal{O})$ and solvable group of all invertible uppertriangular matrices over $\mathcal{O}$, $\text{T}_n(\mathcal{O})$. For each of these groups we provide a complete characterization of arbitrary models of their complete elementary theories.
