Decidability and Computability of Certain Torsion-Free Abelian Groups


Abstract
We study completely decomposable torsion-free abelian groups of the form $\mathcal{G}_S := \oplus_{n \in S} \mathbb{Q}_{p_n}$ for sets $S \subseteq \omega$. We show that $\mathcal{G}_S$has a decidable copy if and only if S is $\Sigma^0_2$and has a computable copy if and only if S is $\Sigma^0_3$
Keywords completely decomposable torsion-free abelian groups   coding in groups
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DOI 10.1215/00294527-2010-006
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References found in this work BETA

Effective Content of Field Theory.G. Metakides & A. Nerode - 1979 - Annals of Mathematical Logic 17 (3):289-320.
Hiearchies of Boolean Algebras.Lawrence Feiner - 1970 - Journal of Symbolic Logic 35 (3):365-374.
The Strong Homogeneity Conjecture.L. Feiner - 1970 - Journal of Symbolic Logic 35 (3):375-377.

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Citations of this work BETA

Degrees of Orders on Torsion-Free Abelian Groups.Asher M. Kach, Karen Lange & Reed Solomon - 2013 - Annals of Pure and Applied Logic 164 (7-8):822-836.
Computable Abelian Groups.Alexander G. Melnikov - 2014 - Bulletin of Symbolic Logic 20 (3):315-356,.

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