Topological properties of definable sets in ordered Abelian groups of burden 2

Abstract We obtain some new results on the topology of unary definable sets in expansions densely ordered Abelian groups burden 2. In special case which structure has dp‐rank 2, we show that existence an infinite discrete set precludes definability a is dense and codense interval, or topologically like Cantor middle‐third (Theorem 2.9). If it 2 both D dense‐codense X are definable, then translates must witness Independence Property 2.26). last section, explicit example group given definable.