## Notre Dame Journal of Formal Logic

### 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 $\Sigma^0_3$.

#### Article information

Source
Notre Dame J. Formal Logic, Volume 51, Number 1 (2010), 85-96.

Dates
First available in Project Euclid: 4 May 2010

https://projecteuclid.org/euclid.ndjfl/1273002111

Digital Object Identifier
doi:10.1215/00294527-2010-006

Mathematical Reviews number (MathSciNet)
MR2666571

Zentralblatt MATH identifier
1211.03063

#### Citation

Downey, Rodney G.; Goncharov, Sergei S.; Kach, Asher M.; Knight, Julia F.; Kudinov, Oleg V.; Melnikov, Alexander G.; Turetsky, Daniel. Decidability and Computability of Certain Torsion-Free Abelian Groups. Notre Dame J. Formal Logic 51 (2010), no. 1, 85--96. doi:10.1215/00294527-2010-006. https://projecteuclid.org/euclid.ndjfl/1273002111

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