A representation theorem for MV-algebras

Abstract

An {\em MV-pair} is a pair $(B,G)$ where $B$ is a Boolean algebra and $G$ is a subgroup of the automorphism group of $B$ satisfying certain conditions. Let $\sim_G$ be the equivalence relation on $B$ naturally associated with $G$. We prove that for every MV-pair $(B,G)$, the effect algebra $B/\sim_G$ is an MV- effect algebra. Moreover, for every MV-effect algebra $M$ there is an MV-pair $(B,G)$ such that $M$ is isomorphic to $B/\sim_G$.