32 citations · 184 across the 63 of their papers we have counts for
8 papers · 1 filter
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…
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…
Undecidability of the first order theories of free non-commutative Lie algebras
Olga Kharlampovich, Alexei Myasnikov
Let be a commutative integral unital domain and a free non-commutative Lie algebra over . In this paper we show that the ring and its action on are 0-interpretab…
What does a group algebra of a free group know about the group?
O. Kharlampovich, A. Miasnikov
We describe solutions to the problem of elementary classification in the class of group algebras of free groups. We will show that unlike free groups, two group algebras of free gr…
Equations in Algebras
Olga Kharlampovich, Alexei Myasnikov
We show that the Diophantine problem(decidability of equations) is undecidable in free associative algebras over any field and in the group algebras over any field of a wide variet…