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Title: Computable torsion abelian groups
Authors: Melnikov, Alexander G.
Ng, Keng Meng
Keywords: Science::Mathematics
Issue Date: 2017
Source: Melnikov, A. G., & Ng, K. M. (2018). Computable torsion abelian groups. Advances in Mathematics, 325, 864-907. doi:10.1016/j.aim.2017.12.011
Journal: Advances in Mathematics
Abstract: We prove that c.c. torsion abelian groups can be described by a Π04-predicate that describes the failure of a brute-force diagonalisation attempt on such groups. We show that there is no simpler description since their index set is Π04-complete. The results can be viewed as a solution to a 60 year-old problem of Mal'cev in the case of torsion abelian groups. We prove that a computable torsion abelian group has one or infinitely many computable copies, up to computable isomorphism. The result confirms a conjecture of Goncharov from the early 1980s for the case of torsion abelian groups.
ISSN: 0001-8708
DOI: 10.1016/j.aim.2017.12.011
Schools: School of Physical and Mathematical Sciences 
Rights: © 2017 Elsevier Inc. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
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