Boris I. Plotkin

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In every variety of algebras Θ we can consider its logic and its algebraic geometry. In the previous papers geometry in equational logic, i.e., equational geometry has been studied. Here we describe an extension of this theory towards the First Order Logic (FOL). The algebraic sets in this geometry are determined by arbitrary sets of FOL formulas. The(More)
The paper is essentially a continuation of [PZ], whose main notion is that of logic-geometrical equivalence of algebras (LG-equivalence of algebras). This equivalence of algebras is stronger than elementary equivalence. In the paper we introduce the notion of isotyped algebras and relate it to LG-equivalence. We show that these notions coincide. The idea of(More)
Some basic notions of classical algebraic geometry can be defined in arbitrary varieties of algebras Θ. For every algebra H in Θ one can consider algebraic geometry in Θ over H. Correspondingly, algebras in Θ are considered with the emphasis on equations and geometry. We give examples of geometric properties of algebras in Θ and of geometric relations(More)
Let Θ 0 be a category of finitly generated free algebras in the variety of algebras Θ. Solutions to problems in algebraic geometry over Θ are often determined by the structure of the group of automorphisms Aut Θ 0 of category Θ 0. Here we consider two varieties Θ: noetherian modules and Lie algebras. We show that every automorphism in Aut Θ 0 , where Θ is(More)