MV-ALGEBRAS AND PARTIALLY CYCLICALLY ORDERED GROUPS

Gérard Leloup (1)

1 LMM - Laboratoire Manceau de Mathématiques

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.

Mots clés: MV-algebras; MV-chains; partially cyclically ordered abelian groups; cyclically ordered abelian groups; pseudofinite

Domaines: Logique [math.LO]; Anneaux et algèbres [math.RA]; Algèbre commutative [math.AC]

Gérard Leloup. MV-ALGEBRAS AND PARTIALLY CYCLICALLY ORDERED GROUPS. 2021. ⟨hal-02016519v2⟩