Chang completeness theorem

Abstract

Translate Article

In this chapter we shall prove Chang’s completeness theorem stating that if an equation holds in the unit real interval [0,1], then the equation holds in every MV-algebra. Thus, intuitively, the two element structure {0,1} stands to boolean algebras as the interval [0,1] stands to MV-algebras. Our proof is elementary, and makes use of tools (such as “good sequences”) that shall also find applications in a subsequent chapter to show the equivalence between MV-algebras and lattice-ordered abelian groups with strong unit.