Hyperbolicity and cubulability are preserved under elementary equivalence

被引：4
|
作者：
Andre, Simon [1 ,2 ]
机构：
[1] Univ Rennes 1, CNRS, IRMAR, UMR 6625, Rennes, France
[2] Vanderbilt Univ, Dept Math, Nashville, TN 37235 USA
来源：
GEOMETRY & TOPOLOGY | 2020年 / 24卷 / 03期
关键词：
DIOPHANTINE GEOMETRY; SUBGROUPS;
D O I：
10.2140/gt.2020.24.1075
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The following properties are preserved under elementary equivalence, among finitely generated groups: being hyperbolic (possibly with torsion), being hyperbolic and cubulable, and being a subgroup of a hyperbolic group. In other words, if a finitely generated group G has the same first-order theory as a group possessing one of the previous properties, then G enjoys that property as well.
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页码：1075 / 1147
页数：73
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