KMS Chongqing Institute of Green and Intelligent Technology, CAS
| Nonexistence of minimal pairs in L[d] | |
Fang, Chengling1; Liu, Jiang2 ; Wu, Guohua3; Yamaleev, Mars M.4
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| 2015 | |
| 摘要 | For a d.c.e. set D with a d.c.e. approximation (Formula presented.), the Lachlan set of D is defined as (Formula presented.). For a d.c.e. degree d, L[d] is defined as the class of c.e. degrees of those Lachlan sets of d.c.e. sets in d. In this paper, we prove that for any proper d.c.e. degree d, no two elements in L[d] can form a minimal pair. This result gives another solution to Ishmukhametov’s problem, which asks whether for any proper d.c.e. degree d, L[d] always has a minimal element. A negative answer to this question was first given by Fang, Wu and Yamaleev in 2013. © Springer International Publishing Switzerland 2015. |
| 语种 | 英语 |
| DOI | 10.1007/978-3-319-20028-6_18 |
| 会议(录)名称 | 11th Conference on Computability in Europe, CiE 2015
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| 页码 | 177-185 |
| 通讯作者 | Wu, Guohua (guohua@ntu.edu.sg) |
| 收录类别 | EI |
| 会议地点 | Bucharest, Romania |
| 会议日期 | June 29, 2015 - July 3, 2015 |
