Geodesic
On definability of completely decomposable torsion-free Abelian groups by certain groups of homomorphisms
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2009), pp. 20-23.

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Let $C$ be an Abelian group. An Abelian group $A$ in some class $X$ of Abelian groups is said to be $_CH$-definable in the class $X$ if for any group $B\in X$ the isomorphism $\mathrm{Hom}(C,A)\cong\mathrm{Hom}(C,B)$ implies that $A\cong B$. If every group in $X$ is $_CH$-definable in $X$, then the class $X$ is called a $_CH$-class. In this paper we study conditions that make a class of completely decomposable torsion-free Abelian groups a $_CH$-class, where $C$ is a vector group.
Keywords: completely decomposable torsion-free Abelian group, vector Abelian group, group of homomorphisms, definability of Abelian groups. 
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T. A. Beregovaya. On definability of completely decomposable torsion-free Abelian groups by certain groups of homomorphisms. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2009), pp. 20-23. http://geodesic.mathdoc.fr/item/IVM_2009_11_a2/

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