Model theory of divisible abelian cyclically ordered groups and minimal C. O. G

TL;DR

This paper explores the model theory of divisible abelian cyclically ordered groups, providing classifications of their theories and analyzing the structure of definable subsets within these groups.

Contribution

It offers a classification of complete theories of divisible abelian cyclically ordered groups and examines the nature of definable subsets in such groups.

Findings

Classification of complete theories of divisible abelian cyclically ordered groups

Analysis of definable subsets as finite unions of singletons and open intervals

Characterization of c-convex subsets in cyclically ordered groups

Abstract

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. 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.