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- B. PLOTKIN
- 2002

- B Plotkin
- 2002

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)

- Boris Plotkin
- 2004

Engel groups and Engel elements became popular in 50s. We consider in the paper the more general nil-groups and nil-elements in groups. All these notions are related to nilpotent groups and nilpo-tent radicals in groups. These notions generate problems which are parallel to Burnside problems for periodic groups. The first three theorems of the paper are… (More)

- BORIS PLOTKIN
- 2009

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)

- B. PLOTKIN
- 2002

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)

- B Plotkin
- 1995

The aim of the paper is discussion of connections between the three kinds of objects named in the title. In a sense, it is a survey of such connections; however, some new directions are also considered. This relates, especially, to sections 3, 4 and 5, where we consider a field that could be understood as an universal algebraic geometry. This geometry is… (More)

- Boris I. Plotkin, Tatjana L. Plotkin
- Pillars of Computer Science
- 2008

- R Lipyanski, B Plotkin
- 2008

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)

In this paper we study the notion of knowledge from the positions of universal algebra and algebraic logic. We consider first order knowledge which is based on first order logic. We define categories of knowledge and knowledge bases. These notions are defined for the fixed subject of knowledge. The key notion of informational equivalence of two knowledge… (More)