Abstract In this paper we study some invariants for MV-algebras and thanks to Mundici's equivalence we transfer these invariants to l-groups with strong unit. In particular, we prove that, as it happens to MV-algebras, every l-u group has two families of skeletons, which we call the n-skeletons and the n-omega- skeletons. Then we study the classes of l-u groups (and of MV-algebras) which coincide with the union of such skeletons, called here omega-skeletal and omega-omega-skeletal l-u groups (resp. MV-algebras). We also analyze the problem of axiomatizing in terms of geometric theories or theories of presheaf type these classes of l-u groups (and of MV-algebras).