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 = 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.