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

Evelina Daniyarova; Alexei Myasnikov

doi:10.1016/j.apal.2025.103695

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

Evelina Daniyarova
, Alexei Myasnikov

Department of Mathematical Sciences

RAS - Sobolev Institute of Mathematics, Siberian Branch

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that metabelian Baumslag – Solitar group BS(1,k), k>1, is (strongly) regularly bi-interpretable with the ring of integers Z, and describe in algebraic terms all groups that are elementarily equivalent to BS(1,k).

Original language	English
Article number	103695
Journal	Annals of Pure and Applied Logic
Volume	177
Issue number	5
DOIs	https://doi.org/10.1016/j.apal.2025.103695
State	Published - May 2026

Keywords

Bi-interpretation
Elementary theory
Exponential group
Metabelian Baumslag – Solitar group
Non-standard model

Access to Document

10.1016/j.apal.2025.103695

Cite this

@article{ec341b87eadb453f908585a8783f7632,

title = "Groups elementarily equivalent to metabelian Baumslag – Solitar groups and regular bi-interpretability",

abstract = "We prove that metabelian Baumslag – Solitar group BS(1,k), k>1, is (strongly) regularly bi-interpretable with the ring of integers Z, and describe in algebraic terms all groups that are elementarily equivalent to BS(1,k).",

keywords = "Bi-interpretation, Elementary theory, Exponential group, Metabelian Baumslag – Solitar group, Non-standard model",

author = "Evelina Daniyarova and Alexei Myasnikov",

note = "Publisher Copyright: {\textcopyright} 2025",

year = "2026",

month = may,

doi = "10.1016/j.apal.2025.103695",

language = "English",

volume = "177",

number = "5",

}

TY - JOUR

T1 - Groups elementarily equivalent to metabelian Baumslag – Solitar groups and regular bi-interpretability

AU - Daniyarova, Evelina

AU - Myasnikov, Alexei

PY - 2026/5

Y1 - 2026/5

N2 - We prove that metabelian Baumslag – Solitar group BS(1,k), k>1, is (strongly) regularly bi-interpretable with the ring of integers Z, and describe in algebraic terms all groups that are elementarily equivalent to BS(1,k).

AB - We prove that metabelian Baumslag – Solitar group BS(1,k), k>1, is (strongly) regularly bi-interpretable with the ring of integers Z, and describe in algebraic terms all groups that are elementarily equivalent to BS(1,k).

KW - Bi-interpretation

KW - Elementary theory

KW - Exponential group

KW - Metabelian Baumslag – Solitar group

KW - Non-standard model

UR - https://www.scopus.com/pages/publications/105024014071

UR - https://www.scopus.com/pages/publications/105024014071#tab=citedBy

U2 - 10.1016/j.apal.2025.103695

DO - 10.1016/j.apal.2025.103695

M3 - Article

AN - SCOPUS:105024014071

SN - 0168-0072

VL - 177

JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

IS - 5

M1 - 103695

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this