A characterization of pseudofinite MV-algebras

Abstract

We consider pseudofinite MV-algebras. As a main result, we show that an infinite MV-algebra is pseudofinite if and only if it is definably well founded, improving a result of a previous paper. Moreover, we show that the theory of pseudofinite MV-algebras has a partial form of elimination of quantifiers. Further, we show that the class of pseudofinite MV-chains and the class of pseudofinite MV-algebras are not finitely axiomatizable, we give some collapsing results for pseudofinite MV-algebras, we consider relative subalgebras of pseudofinite MV-algebras, and we study ideals of pseudofinite MV-algebras.