Natural dualities for varieties generated by finite positive MV-chains

TL;DR

This paper develops a natural duality framework for varieties generated by finite positive MV-chains, enabling detailed analysis of their algebraic properties and relationships with Priestley duality.

Contribution

It introduces a simple natural duality for these varieties and explores their algebraic and duality-theoretic properties in depth.

Findings

Characterization of algebraically closed members

Identification of existentially closed members

Analysis of injective members

Abstract

We provide a simple natural duality for the varieties generated by the negation- and implication- free reduct of a finite MV-chain. We study these varieties through the dual equivalence thus obtained. For example, we fully characterize their algebraically closed, existentially closed and injective members. We also explore the relationship between this natural duality and Priestley duality in terms of distributive skeletons and Priestley powers.