We study completely decomposable torsion-free abelian groups of the form for sets . We show that has a decidable copy if and only if S is and has a computable copy if and only if S is .
"Decidability and Computability of Certain Torsion-Free Abelian Groups." Notre Dame J. Formal Logic 51 (1) 85 - 96, 2010. https://doi.org/10.1215/00294527-2010-006