4 found
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  1.  34
    Isolation and the High/Low Hierarchy.Shamil Ishmukhametov & Guohua Wu - 2002 - Archive for Mathematical Logic 41 (3):259-266.
    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 (...)
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  2.  34
    On the R.E. Predecessors of D.R.E. Degrees.Shamil Ishmukhametov - 1999 - Archive for Mathematical Logic 38 (6):373-386.
    Let d be a Turing degree containing differences of recursively enumerable sets (d.r.e.sets) and R[d] be the class of less than d r.e. degrees in whichd is relatively enumerable (r.e.). A.H.Lachlan proved that for any non-recursive d.r.e. d R[d] is not empty. We show that the r.e. degree defined by Lachlan for a d.r.e.set $D\in$ d is just the minimum degree in which D is r.e. Then we study for a given d.r.e. degree d class R[d] and show that there (...)
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  3.  32
    On a Problem of Cooper and Epstein.Shamil Ishmukhametov - 2003 - Journal of Symbolic Logic 68 (1):52-64.
    In "Bounding minimal degrees by computably enumerable degrees" by A. Li and D. Yang, (this Journal, [1998]), the authors prove that there exist non-computable computably enumerable degrees c > a > 0 such that any minimal degree m being below c is also below a. We analyze the proof of their result and show that the proof contains a mistake. Instead we give a proof for the opposite result.
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  4.  9
    On Relative Enumerability of Turing Degrees.Shamil Ishmukhametov - 2000 - Archive for Mathematical Logic 39 (3):145-154.
    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 (...)
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