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 C of Abelian groups. We show that G is determined up to quasi-isomorphism if C is the class of all self-small mixed groups C with r(0)(C) <= r(0)(G). Several related results are given, and the dual problem of orthogonal classes is investigated.
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