Strong theories of ordered Abelian groups
Volume 236 / 2017
Fundamenta Mathematicae 236 (2017), 269-296
MSC: Primary 03C45; Secondary 03C64.
DOI: 10.4064/fm256-5-2016
Published online: 14 October 2016
Abstract
We consider strong expansions of the theory of ordered Abelian groups. We show that the assumption of strength has a multitude of desirable consequences for the structure of definable sets in such theories, in particular as relates to definable infinite discrete sets. We also provide a range of examples of strong expansions of ordered Abelian groups which demonstrate the great variety of such theories.
