Notre Dame Journal of Formal Logic

Decidability and Computability of Certain Torsion-Free Abelian Groups

Rodney G. Downey, Sergei S. Goncharov, Asher M. Kach, Julia F. Knight, Oleg V. Kudinov, Alexander G. Melnikov, and Daniel Turetsky

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

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1273002111

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

Mathematical Reviews number (MathSciNet)
MR2666571

Zentralblatt MATH identifier
05720471

Subjects
Primary: 03D45: Theory of numerations, effectively presented structures [See also 03C57; for intuitionistic and similar approaches see 03F55]

Keywords
completely decomposable torsion-free abelian groups coding in groups

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


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