  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 lattice-ordered 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.
