A Stone-Weierstrass theorem for MV-algebras and unital l-groups

Working jointly in the equivalent categories of MV-algebras and lattice-ordered abelian groups with strong order unit (for short, unital l-groups), we prove that isomorphism is a sufficient condition for a separating subalgebra A of a finitely presented algebra F to coincide with F. The separation and isomorphism conditions do not individually imply A= F. Various related problems, like the separation property of A, or A congruent to F (for A a separating subalgebra of F), are shown to be (Turing-) decidable. We use tools from algebraic topology, category theory, polyhedral geometry and computational algebraic logic.