c-regular cyclically ordered groups

Gérard Leloup (1) , Francois Lucas (2)

1 LMM - Laboratoire Manceau de Mathématiques
2 LAREMA - Laboratoire Angevin de Recherche en Mathématiques

We define and we characterize regular and c-regular cyclically ordered abelian groups. We prove that every dense c-regular cyclically ordered abelian group is elementarily equivalent to some cyclically ordered group of unimodular complex numbers, that every discrete c-regular cyclically ordered abelian group is elementarily equivalent to some ultraproduct of finite cyclic groups, and that the discrete regular non-c-regular cyclically ordered abelian groups are elementarily equivalent to the linearly cyclically ordered group of integers.

Mots clés: Abelian cyclically ordered groups; regular; cyclic groups; groups of unimodular complex numbers; first order theory.; first order theory

Domaines: Logique [math.LO]

Gérard Leloup, Francois Lucas. c-regular cyclically ordered groups. 2013. ⟨hal-00919983⟩