Decidability and Computability of Certain Torsion-Free Abelian Groups

Abstract

We study completely decomposable torsion-free abelian groups of the form G S : = ⊕ n ∈ S ℚ p n for sets S ⊆ ω . We show that G S has a decidable copy if and only if S is Σ 2 0 and has a computable copy if and only if S is Σ 3 0 .