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 ω-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).
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Di Nola, A., Lenzi, G. & Russo, A.C. Some Invariant Skeletons for ℓ-u Groups and MV-Algebras. Order 36, 77–97 (2019). https://doi.org/10.1007/s11083-018-9456-5
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DOI: https://doi.org/10.1007/s11083-018-9456-5