Decidability and Computability of Certain Torsion-Free Abelian Groups

Notre Dame Journal of Formal Logic 51 (1):85-96 (2010)
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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 $\Sigma^0_3$

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Author Profiles

Alexander Melnikov
National Research University Higher School of Economics

Citations of this work

Computable Abelian groups.Alexander G. Melnikov - 2014 - Bulletin of Symbolic Logic 20 (3):315-356,.
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.

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References found in this work

Computable structures and the hyperarithmetical hierarchy.C. J. Ash - 2000 - New York: Elsevier. Edited by J. Knight.
Hiearchies of Boolean algebras.Lawrence Feiner - 1970 - Journal of Symbolic Logic 35 (3):365-374.
Effective content of field theory.G. Metakides - 1979 - Annals of Mathematical Logic 17 (3):289.
The strong homogeneity conjecture.L. Feiner - 1970 - Journal of Symbolic Logic 35 (3):375-377.

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