This paper investigates to which extent a self-small mixed Abelian group G of finite torsion-free rank is determined by the groups Hom (G,C) where C is chosen from a suitable class [Formula: see text] of Abelian groups. We show that G is determined up to quasi-isomorphism if [Formula: see text] is the class of all self-small mixed groups C with r0(C) ≤ r0(G). Several related results are given, and the dual problem of orthogonal classes is investigated.
