On a problem of Ishmukhametov
Given a d.c.e. degree d, consider the d.c.e. sets in d and the corresponding degrees of their Lachlan sets. Ishmukhametov provided a systematic investigation of such degrees, and proved that for a given d.c.e. degree d > 0, the class of its c.e. predecessors in which d is c.e., denoted as R[d], c...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2014
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/103046 http://hdl.handle.net/10220/19230 |
| _version_ | 1811697533279272960 |
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| author | Yamaleev, Mars Fang, Chengling Wu, Guohua |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Yamaleev, Mars Fang, Chengling Wu, Guohua |
| author_sort | Yamaleev, Mars |
| collection | NTU |
| description | Given a d.c.e. degree d, consider the d.c.e. sets in d and the corresponding degrees of their Lachlan sets. Ishmukhametov provided a systematic investigation of such degrees, and proved that for a given d.c.e. degree d > 0, the class of its c.e. predecessors in which d is c.e., denoted as R[d], can consist of either just one element, or an interval of c.e. degrees. After this, Ishmukhametov asked whether there exists a d.c.e. degree d for which the class R[d] has no minimal element. We give a positive answer to this question. |
| first_indexed | 2024-10-01T07:56:46Z |
| format | Journal Article |
| id | ntu-10356/103046 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:56:46Z |
| publishDate | 2014 |
| record_format | dspace |
| spelling | ntu-10356/1030462020-03-07T12:34:45Z On a problem of Ishmukhametov Yamaleev, Mars Fang, Chengling Wu, Guohua School of Physical and Mathematical Sciences DRNTU::Science::Mathematics Given a d.c.e. degree d, consider the d.c.e. sets in d and the corresponding degrees of their Lachlan sets. Ishmukhametov provided a systematic investigation of such degrees, and proved that for a given d.c.e. degree d > 0, the class of its c.e. predecessors in which d is c.e., denoted as R[d], can consist of either just one element, or an interval of c.e. degrees. After this, Ishmukhametov asked whether there exists a d.c.e. degree d for which the class R[d] has no minimal element. We give a positive answer to this question. 2014-04-10T06:36:53Z 2019-12-06T21:04:24Z 2014-04-10T06:36:53Z 2019-12-06T21:04:24Z 2013 2013 Journal Article Fang, C., Wu, G., Yamaleev, M. (2013). On a problem of Ishmukhametov. Archive for Mathematical Logic, 52(7-8), 733-741. https://hdl.handle.net/10356/103046 http://hdl.handle.net/10220/19230 10.1007/s00153-013-0340-0 177265 en Archive for mathematical logic © 2013 Springer-Verlag Berlin Heidelberg. |
| spellingShingle | DRNTU::Science::Mathematics Yamaleev, Mars Fang, Chengling Wu, Guohua On a problem of Ishmukhametov |
| title | On a problem of Ishmukhametov |
| title_full | On a problem of Ishmukhametov |
| title_fullStr | On a problem of Ishmukhametov |
| title_full_unstemmed | On a problem of Ishmukhametov |
| title_short | On a problem of Ishmukhametov |
| title_sort | on a problem of ishmukhametov |
| topic | DRNTU::Science::Mathematics |
| url | https://hdl.handle.net/10356/103046 http://hdl.handle.net/10220/19230 |
| work_keys_str_mv | AT yamaleevmars onaproblemofishmukhametov AT fangchengling onaproblemofishmukhametov AT wuguohua onaproblemofishmukhametov |