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Some Invariant Skeletons for -u Groups and MV-Algebras

  • Antonio Di Nola
  • Giacomo Lenzi
  • Anna Carla Russo
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Abstract

In this paper we study some invariants for MV-algebras and thanks to Mundici’s equivalence we transfer these invariants to -groups with strong unit. In particular, we prove that, as it happens to MV-algebras, every -u group has two families of skeletons, which we call the n-skeletons and the \({}_{n}^{\omega }\)-skeletons. Then we study the classes of -u groups (and of MV-algebras) which coincide with the union of such skeletons, called here ω-skeletal and \({}_{\omega }^{\omega }\)-skeletal -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 -u groups (and of MV-algebras).

Keywords

MV-algebra Lattice ordered Abelian group with strong unit Skeleton Geometric theory 

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  • Antonio Di Nola
    • 1
    • 2
  • Giacomo Lenzi
    • 1
  • Anna Carla Russo
    • 3
  1. 1.University of SalernoFiscianoItaly
  2. 2.I.I.A.S.S. “E. R. Caianiello”Vietri sul mareItaly
  3. 3.PaganiItaly

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