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On the r.e. predecessors of d.r.e. degrees

Shamil Ishmukhametov

Archive for Mathematical Logic 38 (6):373-386 (1999)

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On a problem of Ishmukhametov.Chengling Fang, Guohua Wu & Mars Yamaleev - 2013 - Archive for Mathematical Logic 52 (7-8):733-741.details 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] (...) Download Export citation Bookmark
Isolation and the high/low hierarchy.Shamil Ishmukhametov & Guohua Wu - 2002 - Archive for Mathematical Logic 41 (3):259-266.details Say that a d.c.e. degree d is isolated by a c.e. degree b, if bMathematics Subject Classification (2000): 03D25, 03D30, 03D35 RID=""ID="" Key words or phrases: Computably enumerable (...) Download Export citation Bookmark 11 citations
On relative enumerability of Turing degrees.Shamil Ishmukhametov - 2000 - Archive for Mathematical Logic 39 (3):145-154.details Let d be a Turing degree, R[d] and Q[d] denote respectively classes of recursively enumerable (r.e.) and all degrees in which d is relatively enumerable. We proved in Ishmukhametov [1999] that there is a degree d containing differences of r.e.sets (briefly, d.r.e.degree) such that R[d] possess a least elementm $>$ 0. Now we show the existence of a d.r.e. d such that R[d] has no a least element. We prove also that for any REA-degree d below 0 $'$ the class (...) Download Export citation Bookmark 1 citation

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