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 $\Sigma^0_3$ .
Publié le : 2010-01-15
Classification:
completely decomposable torsion-free abelian groups,
coding in groups,
03D45
@article{1273002111,
author = {Downey, Rodney G. and Goncharov, Sergei S. and Kach, Asher M. and Knight, Julia F. and Kudinov, Oleg V. and Melnikov, Alexander G. and Turetsky, Daniel},
title = {Decidability and Computability of Certain Torsion-Free Abelian Groups},
journal = {Notre Dame J. Formal Logic},
volume = {51},
number = {1},
year = {2010},
pages = { 85-96},
language = {en},
url = {http://dml.mathdoc.fr/item/1273002111}
}
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, Tome 51 (2010) no. 1, pp. 85-96. http://gdmltest.u-ga.fr/item/1273002111/