论文标题
关于高级算术组的模型理论
On the model theory of higher rank arithmetic groups
论文作者
论文摘要
令$γ$为特征零的无中心不可还原的高级算术晶格。我们证明，如果$γ$是不均匀的，或者至少是正交类型和尺寸均匀的，那么$γ$与整数的$ \ mathbb {z} $相比，$γ$是双式交换。因此，$γ$的一阶理论是不可确定的，所有有限生成的亚组的$γ$都是可定义的，并且$γ$的特征是在所有有限生成的群体中单一的一阶句子。
Let $Γ$ be a centerless irreducible higher rank arithmetic lattice in characteristic zero. We prove that if $Γ$ is either non-uniform or is uniform of orthogonal type and dimension at least 9, then $Γ$ is bi-interpretable with the ring $\mathbb{Z}$ of integers. It follows that the first order theory of $Γ$ is undecidable, that all finitely generated subgroups of $Γ$ are definable, and that $Γ$ is characterized by a single first order sentence among all finitely generated groups.
