Algebraic Logic, Varieties of Algebras and Algebraic Varieties

TL;DR

This paper explores the relationships between algebraic logic, varieties of algebras, and algebraic varieties, highlighting their connections and introducing new directions in universal algebraic geometry.

Contribution

It provides a survey of the relations among these objects and proposes new perspectives in universal algebraic geometry.

Findings

Identifies connections between algebraic logic and algebraic varieties.

Introduces new directions in universal algebraic geometry.

Highlights parallels between universal algebra and algebraic geometry.

Abstract

The aim of the paper is to discuss the relations between the three kinds of objects named in the title. In a sense, this is a survey of such relations; however, some new directions are also considered. This relates, especially, to sections 3, 4 and 5, where we consider the universal algebraic geometry. This geometry is parallel to universal algebra.