Computable torsion abelian groups
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-o...
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sg-ntu-dr.10356-1376802020-04-08T04:37:33Z Computable torsion abelian groups Melnikov, Alexander G. Ng, Keng Meng School of Physical and Mathematical Sciences Science::Mathematics Abelian Groups Computable Structures 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. MOE (Min. of Education, S’pore) 2020-04-08T04:37:33Z 2020-04-08T04:37:33Z 2017 Journal Article 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 0001-8708 https://hdl.handle.net/10356/137680 10.1016/j.aim.2017.12.011 2-s2.0-85040577940 325 864 907 en Advances in Mathematics © 2017 Elsevier Inc. All rights reserved. |
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Science::Mathematics Abelian Groups Computable Structures |
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Science::Mathematics Abelian Groups Computable Structures Melnikov, Alexander G. Ng, Keng Meng Computable torsion abelian groups |
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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. |
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School of Physical and Mathematical Sciences |
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School of Physical and Mathematical Sciences Melnikov, Alexander G. Ng, Keng Meng |
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Article |
| author |
Melnikov, Alexander G. Ng, Keng Meng |
| author_sort |
Melnikov, Alexander G. |
| title |
Computable torsion abelian groups |
| title_short |
Computable torsion abelian groups |
| title_full |
Computable torsion abelian groups |
| title_fullStr |
Computable torsion abelian groups |
| title_full_unstemmed |
Computable torsion abelian groups |
| title_sort |
computable torsion abelian groups |
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2020 |
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https://hdl.handle.net/10356/137680 |
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