Elementary equivalence of right-angled Coxeter groups and graph products of finite abelian groups

Abstract

We show that graph products of finite abelian groups are elementarily equivalent if and only if they are $\exists \forall$-equivalent if and only if they are isomorphic. In particular, two right-angled Coxeter groups are elementarily equivalent if and only if they are isomorphic.

arXiv comment7 pages; version 2: added a reference to David Radcliffe's rigidity result and Remark 2.4

Cited by in corpus (3)

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• Nonstandard analysis, deformation quantization and some logical aspects of (non)commutative algebraic geometry
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