On first order rigidity for linear groups

Abstract

The paper is a short survey of recent developments in the area of first order descriptions of linear groups. It is aimed to illuminate the known results and to pose the new problems relevant to logical characterizations of Chevalley groups and Kac-Moody groups.

9 pages. arXiv admin note: substantial text overlap with arXiv:2008.09788

References in corpus (5)

• Simplicity and superrigidity of twin building lattices
• Algebras with the same (algebraic) geometry
• Homogeneity in the free group
• On the model theory of higher rank arithmetic groups
• Bi-interpretability with $\mathbb{Z}$ and models of the complete elementary theories of ${\text{SL}}_n(\mathcal{O})$, ${\text{T}}_n(\mathcal{O})$ and ${\text{GL}}_n(\mathcal{O})$, $n\ge 3$