Representation of Perfect and Local MV-algebras

We describe representation theorems for local and perfect MV-algebras in terms of ultraproducts involving the unit interval [0, 1]. Furthermore, we give a representation of local Abelian ℓ-groups with strong unit as quasi-constant functions on an ultraproduct of the reals. All the above theorems are proved to have a uniform version, depending only on the cardinality of the algebra to be embedded, as well as a definable construction in ZFC. The paper contains both known and new results and provides a complete overview of representation theorems for such classes.