Two Remarks on First-Order Theories of Baumslag-Solitar Groups

Abstract

In this note we characterise all finitely generated groups elementarily equivalent to a solvable Baumslag-Solitar group BS$(1,n)$. It turns out that a finitely generated group $G$ is elementarily equivalent to BS$(1,n)$ if and only if $G$ is isomorphic to BS$(1,n)$. Furthermore, we show that two Baumslag-Solitar groups are existentially (universally) equivalent if and only if they are elementarily equivalent if and only if they are isomorphic.

arXiv comment5 pages, no figures. Version 3 corrects a mistake pointed out to us by G. Levitt

Cited by in corpus (1)

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