Riesz–McNaughton functions and Riesz MV-algebras of nonlinear functions

Abstract

We focus on Riesz MV-algebras, which are MV-algebras equipped with a multiplication by numbers in the real interval [0,1]. We consider for every integer n the Riesz MV-algebra of all continuous functions from the n-th power of [0,1] to [0,1] and the Riesz MV-subalgebras thereof. In particular we study the Riesz MV-subalgebras isomorphic to free Riesz MV-algebras with finitely many generators, possibly different from the usual linear models given by what we call Riesz–McNaughton functions (and which generalize McNaughton functions used in the case of MV-algebras). In doing this we characterize zerosets of Riesz–McNaughton functions by means of polyhedra, and we extend to Riesz MV-algebras a duality for MV-algebras exposed in a paper by Marra and Spada.