This article is cited in 3 papers

Mathematical logic, algebra and number theory

On some of logical closures on universal algebras

A. G. Pinus

Novosibirsk State Technical University, pr. K. Marxa, 20, 630073, Novosibirsk, Russia

Abstract: B.I. Plotkin has introduced some concepts of logical geometries on universal algebras. Here we study one of the related logical closure operators on sets of elements of an algebra definable by quantifier–free formulas using some quasiorder on the basic set of this algebra.

Keywords: algebraic geometry, universal algebra, closure operator.

UDC: 517.53,517.55

MSC: 32A10,46E15

Received February 5, 2015, published October 5, 2015

DOI: 10.17377/semi.2015.12.055