MV-ALGEBRAS AND PARTIALLY CYCLICALLY ORDERED GROUPS - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2019

MV-ALGEBRAS AND PARTIALLY CYCLICALLY ORDERED GROUPS

Gérard Leloup

Résumé

We prove that there exists a functorial correspondence between MV-algebras and partially cyclically ordered groups which are wound round of lattice-ordered groups. It follows that some results about cyclically ordered groups can be stated in terms of MV-algebras. For example, the study of groups together with a cyclic order allows to get a first-order characterization of groups of unimodular complex numbers and of finite cyclic groups. We deduce a characterization of pseudofinite MV-chains and of pseudo-simple MV-chains (i.e. which share the same first-order properties as some simple ones). We can generalize these results to some non-lineraly ordered MV-algebras, for example hyper-archimedean MV-algebras.
Fichier principal
Vignette du fichier
MVAPCO18.pdf (387.39 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-02016519 , version 1 (12-02-2019)
hal-02016519 , version 2 (09-06-2021)

Identifiants

Citer

Gérard Leloup. MV-ALGEBRAS AND PARTIALLY CYCLICALLY ORDERED GROUPS. 2019. ⟨hal-02016519v1⟩
69 Consultations
145 Téléchargements

Altmetric

Partager

More