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...
| প্রধান লেখক: | , |
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| অন্যান্য লেখক: | |
| বিন্যাস: | Journal Article |
| ভাষা: | English |
| প্রকাশিত: |
2020
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| বিষয়গুলি: | |
| অনলাইন ব্যবহার করুন: | https://hdl.handle.net/10356/137680 |
| _version_ | 1826125216048218112 |
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| author | Melnikov, Alexander G. Ng, Keng Meng |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Melnikov, Alexander G. Ng, Keng Meng |
| author_sort | Melnikov, Alexander G. |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T06:33:04Z |
| format | Journal Article |
| id | ntu-10356/137680 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T06:33:04Z |
| publishDate | 2020 |
| record_format | dspace |
| spelling | ntu-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. |
| spellingShingle | Science::Mathematics Abelian Groups Computable Structures Melnikov, Alexander G. Ng, Keng Meng Computable torsion abelian groups |
| title | Computable torsion abelian groups |
| title_full | Computable torsion abelian groups |
| title_fullStr | Computable torsion abelian groups |
| title_full_unstemmed | Computable torsion abelian groups |
| title_short | Computable torsion abelian groups |
| title_sort | computable torsion abelian groups |
| topic | Science::Mathematics Abelian Groups Computable Structures |
| url | https://hdl.handle.net/10356/137680 |
| work_keys_str_mv | AT melnikovalexanderg computabletorsionabeliangroups AT ngkengmeng computabletorsionabeliangroups |