On Fidel Vakarelov construction for Monadic Godel algebras

TL;DR

This paper extends the Fidel-Vakarelov construction to monadic Godel algebras, introducing a new variety called monadic prelinear Nelson algebras, thereby deepening the understanding of algebraic structures related to logic.

Contribution

It provides an expanded Fidel-Vakarelov construction applicable to monadic Godel algebras, resulting in the novel class of monadic prelinear Nelson algebras.

Findings

Introduction of monadic prelinear Nelson algebras

Extension of Fidel-Vakarelov construction to new algebraic structures

Establishment of a new variety in algebraic logic

Abstract

A significant correlation between Nelson algebras and Heyting algebras has been explored by several scholars, including Cignoli, Fidel, Vakarelov, and Sendlewski. This connection is integral to the concept of twist structures, whose origins can be traced back to the work of Kalman. In this paper, we obtain an expansion of the Fidel-Vakarelov construction, applying it to monadic Godel algebras (or monadic prelinear Heyting algebras). This extension leads to the emergence of a new variety, which we aptly term monadic prelinear Nelson algebras.