Finite Axiomatisability of Subdirectly Irreducible Members of Certain Nilpotent Varieties

TL;DR

This paper proves that for certain finite nilpotent algebra-generated varieties, the class of subdirectly irreducible members can be finitely axiomatized, advancing understanding of algebraic structure and logical definability.

Contribution

It establishes finite axiomatisability of subdirectly irreducible members in specific nilpotent varieties generated by prime power order algebras.

Findings

Finite axiomatization of subdirectly irreducible members

Applicable to varieties generated by product of prime power order algebras

Advances in algebraic logic and structural theory

Abstract

Let $\mathcal{V}$ be a congruence permutable variety generated by a finite nilpotent algebra $\mathbf{A}$. If $\mathbf{A}$ is a product of algebras of prime power order, then the class $\mathcal{V}_\text{si}$ of subdirectly irreducible members of $\mathcal{V}$ can be axiomatised by a finite set of elementary sentences.