MODEL THEORY OF DIVISIBLE ABELIAN CYCLICALLY ORDERED GROUPS AND MINIMAL C. O. G

Gérard Leloup (1)

1 LMM - Laboratoire Manceau de Mathématiques

We make available some results about model theory cyclically ordered groups. We start with a classification of complete theories of divisible abelian cyclically ordered groups. Most of this paper is dedicated to the study of the model theory of torsion-free divisible abelian cyclically ordered groups, since we first show that the theory of divisible abelian cyclically ordered groups with non-trivial torsion elements is complete. Then we look at the cyclically ordered groups where the only parametrically definable subsets are finite unions of singletons and open intervals, and those where the definable subsets are finite union of singletons and c-convex subsets, where being c-convex is the analogue of being convex in the linearly ordered case.

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

Gérard Leloup. MODEL THEORY OF DIVISIBLE ABELIAN CYCLICALLY ORDERED GROUPS AND MINIMAL C. O. G. 2021. ⟨hal-03254697v1⟩