32 citations · 184 across the 63 of their papers we have counts for
78 papers
Groups elementarily equivalent to the classical matrix groups
Alexei G. Myasnikov, Mahmood Sohrabi
In this paper we describe all groups that are first-order (elementarily) equivalent to the classical matrix groups such as and over a field provided…
Rich groups, weak second order logic, and applications
Olga Kharlampovich, Alexei Myasnikov, Mahmood Sohrabi
In this paper we initiate a study of first-order rich groups, i.e., groups where the first-order logic has the same power as the weak second order logic. Surprisingly, there are qu…
Bi-interpretability with and models of the complete elementary theories of , and ,
Mahmood Sohrabi, Alexei G. Myasnikov
Let be the ring of integers of a number field, and let . This paper studies bi-interpretability of the ring of integers with the special linear…
Diophantine Problem in Some Metabelian Groups
Olga Kharlampovich, Laura Lopez, Alexei Miasnikov
In this paper we show that Diophantine problem for quadratic equations in Baumslag-Solitar groups and in wreath products , where is a finitely gener…
Fraïssé limits of limit groups
Olga Kharlampovich, Alexei Myasnikov, Rizos Sklinos
We modify the notion of a Fraïssé class and show that various interesting classes of groups, notably the class of nonabelian limit groups and the class of finitely generated elemen…
Undecidability of Equations in Free Lie Algebras
Olga Kharlampovich, Alexei Myasnikov
In this paper we prove undecidability of finite systems of equations in free Lie algebras of rank at least three over an arbitrary field. We show that the ring of integers $\mathbb…