Some Invariant Skeletons for ℓ-u Groups and MV-Algebras

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 nω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${}_{n}^{\omega }$\end{document}-skeletons. Then we study the classes of ℓ-u groups (and of MV-algebras) which coincide with the union of such skeletons, called here ω-skeletal and ωω\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${}_{\omega }^{\omega }$\end{document}-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).