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https://hdl.handle.net/10356/137680
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. | URI: | https://hdl.handle.net/10356/137680 | 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 |
Appears in Collections: | SPMS Journal Articles |
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