Left-ordered inp-minimal groups

We prove that any left-ordered inp-minimal group is abelian, and we provide an example of a non-abelian left-ordered group of dp-rank 2

Dp-minimality: basic facts and examples

We study the notion of dp-minimality, beginning by providing several essential facts, establishing several equivalent definitions, and comparing dp-minimality to other minimality notions. The rest of the paper is dedicated to examples. We establish via a simple proof that any weakly o-minimal theory is dp-minimal and then give an example of a weakly o-minimal group not obtained by adding traces of externally definable sets. Next we give an example of a divisible ordered Abelian group which is dp-minimal and not weakly o-minimal. Finally we establish that the field of p-adic numbers is dp-minimal.Comment: 19 pages; simplified proof for the p-adic

SETS DEFINABLE IN ORDERED ABELIAN GROUPS OF FINITE BURDEN (Model theoretic aspects of the notion of independence and dimension)

In this note, we survey some recent results on definable sets in ordered Abelian groups of finite burden, focusing on topological and arithmetical tameness properties. In the burden 2 case, and assuming definably completeness, definable discrete subsets of the universe can be characterized as those which are definable in an expansion which is elementarily equivalent to (ℝ;<, +, ℤ). We end with some open questions and possible directions for future research