Algebraic logic and logical geometry in arbitrary varieties of algebras

TL;DR

This paper explores the intersection of algebraic logic and universal algebraic geometry across various algebraic varieties, presenting foundational ideas and preliminary results for a comprehensive upcoming book.

Contribution

It introduces a framework connecting algebraic logic with geometric methods in arbitrary algebraic varieties, advancing the theoretical foundation of universal algebraic geometry.

Findings

Develops a logical approach to algebraic geometry in diverse algebraic structures

Provides initial results on problems in algebraic logic and geometry

Sets the stage for a comprehensive theory in a forthcoming book

Abstract

The paper consists of two parts. The first part is devoted to logic for universal algebraic geometry. The second one deals with problems and some results. It may be regarded as a brief exposition of some ideas from the book in progress: B.Plotkin, E.Aladova, E.Plotkin, "Algebraic logic and logical geometry in arbitrary varieties of algebras"