Related papers: On some open problems in Algebraic logic

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

Enveloping algebras of Hom-Lie and Hom-Leibniz algebras are constructed.

The Jacobian algebras are introduced and their various properties are studied.

We discuss several open problems on spectrally bounded operators, some new, some old, adding in a few new insights.

The article explores the arithmetic of multiplication as a model of many valued projective logic. It is demonstrated that closed numerical intervals within this framework constitute Heyting algebras. The conditions for these algebras to be…

We survey some principal results and open problems related to colorings of algebraic and geometric objects endowed with symmetries.

The chapter provides an introduction to the basic concepts of Algebraic Topology with an emphasis on motivation from applications in the physical sciences. It finishes with a brief review of computational work in algebraic topology,…

We introduce a variation on Barthe et al.'s higher-order logic in which formulas are interpreted as predicates over open rather than closed objects. This way, concepts which have an intrinsically functional nature, like continuity,…

New cases of the multiplicity conjecture are considered.

Symmetries and reductions of some algebraic equations are considered. Transformations that preserve the form of several algebraic equations, as well as transformations that reduce the degree of these equations, are described. Illustrative…

We study an extension of \g propositional logic whose corresponding algebra is an ordered Abelian group. Then we expand the ideas to first-order case of this logic.

Basic arithmetic is the cornerstone of mathematics and computer sciences. In arithmetic, 'division by zero' is an undefined operation and any attempt at extending logic for algebraic division to incorporate division by zero has resulted in…

The aim of this work is to develop a study from the perspective of Abstract Algebraic Logic of some bilattice-based logical systems introduced in the nineties by Ofer Arieli and Arnon Avron. The motivation for such an investigation has two…

We consider the problem of counting the number of answers to a first-order formula on a finite structure. We present and study an extension of first-order logic in which algorithms for this counting problem can be naturally and conveniently…

In this paper we investigate two logics from an algebraic point of view. The two logics are: MALL (multiplicative-additive Linear Logic) and LL (classical Linear Logic). Both logics turn out to be strongly algebraizable in the sense of Blok…

A brief and elementary introduction to the subject is presented. Two open problems are given.

We propose an algebraic geometric approach for studying rational solutions of first-order algebraic ordinary difference equations. For an autonomous first-order algebraic ordinary difference equations, we give an upper bound for the degrees…

We prove that algebraic isomorphisms between limit algebras are automatically continuous, and consider consequences of this result. In particular, we give partial solutions to a conjecture of Power [Limit Algebras, Longman, 1992, Notes to…

Some simple nonlinear recursions which can be completely managed are identified and the behaviour of all their solutions is ascertained.

The main objective of this paper is to show that the notion of type which was developed within the frames of logic and model theory has deep ties with geometric properties of algebras. These ties go back and forth from universal algebraic…