Is being a higher rank lattice a first order property?

We show that there is a sentence \(\varphi\) in the first order language of groups such that a finitely generated group \(\Gamma\) satisfies \(\varphi\) if and only if \(\Gamma\) is isomorphic to a group of the form \(\mathrm{PSL}_n(O)\), where \(n \geq 3\) and \(O\) is a ring of \(S\)-integers in a...

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Bibliographic Details
Published in:arXiv.org 2020-10
Main Authors: Avni, Nir, Chen Meiri
Format: Article
Language:English
Subjects:
Number theory
Online Access:Get full text
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Summary:We show that there is a sentence \(\varphi\) in the first order language of groups such that a finitely generated group \(\Gamma\) satisfies \(\varphi\) if and only if \(\Gamma\) is isomorphic to a group of the form \(\mathrm{PSL}_n(O)\), where \(n \geq 3\) and \(O\) is a ring of \(S\)-integers in a number field.
ISSN:2331-8422