10 citations · 11 across the 5 of their papers we have counts for
6 papers
Theory of Interpretations II. Categorical equivalence of projective logical geometries
Evelina Daniyarova, Alexei Myasnikov
We introduce projective logical geometry and prove that two algebraic structures are strongly bi-interpretable if and only if their categories of projective logical sets are equiva…
Theory of Interpretations I. Foundations
Evelina Daniyarova, Alexei Myasnikov
This is the first paper in a series in which we lay down the foundations of the theory of interpretations. We systematically study different types of interpretations and their prop…
Andrews-Curtis groups
Robert H. Gilman, Alexei G. Myasnikov
For any group and integer the Andrews-Curtis transformations act as a permutation group, termed the Andrews-Curtis group , on the subset …
Groups elementarily equivalent to metabelian BaumslagSolitar groups and regular bi-interpretability
Evelina Daniyarova, Alexei Myasnikov
We prove that metabelian BaumslagSolitar group , , is (strongly) regularly bi-interpretable with the ring of integers , and describe in algebraic terms…
Algebraic geometry over algebraic structures II: Foundations
Evelina Daniyarova, Alexei Myasnikov, Vladimir Remeslennikov
In this paper we introduce elements of algebraic geometry over an arbitrary algebraic structure. We prove Unification Theorems which gather the description of coordinate algebras b…
Unification theorems in algebraic geometry
E. Daniyarova, A. Myasnikov, V. Remeslennikov
In this paper, for a given finitely generated algebra (an algebraic structure with arbitrary operations and no predicates) A we study finitely generated limit algebras of A, approa…