On Fidel Vakarelov construction for Monadic Godel algebras

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.