Submission date: 26 November 2015

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.

Mathematics Subject Classification: 03C45, 03C64

Keywords and phrases: Ordered groups, abelian groups, NIP, strongly dependent theories.

Full text arXiv 1511.08274: pdf, ps.