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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| Main Authors: | , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
2020
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/137680 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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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