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Title: On a problem of Ishmukhametov
Authors: Yamaleev, Mars
Fang, Chengling
Wu, Guohua
Keywords: DRNTU::Science::Mathematics
Issue Date: 2013
Source: Fang, C., Wu, G., Yamaleev, M. (2013). On a problem of Ishmukhametov. Archive for Mathematical Logic, 52(7-8), 733-741.
Series/Report no.: Archive for mathematical logic
Abstract: 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.
DOI: 10.1007/s00153-013-0340-0
Rights: © 2013 Springer-Verlag Berlin Heidelberg.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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