Groups elementarily equivalent to metabelian Baumslag$-$Solitar groups and regular bi-interpretability

Evelina Daniyarova, Alexei Myasnikov

We prove that metabelian Baumslag$-$Solitar group $BS(1,k)$, $k>1$, is (strongly) regularly bi-interpretable with the ring of integers $\mathbb{Z}$, and describe in algebraic terms…