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  1. 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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  • 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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  • Relative enumerability in the difference hierarchy.Marat M. Arslanov, Geoffrey L. Laforte & Theodore A. Slaman - 1998 - Journal of Symbolic Logic 63 (2):411-420.
    We show that the intersection of the class of 2-REA degrees with that of the ω-r.e. degrees consists precisely of the class of d.r.e. degrees. We also include some applications and show that there is no natural generalization of this result to higher levels of the REA hierarchy.
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  • Relative Enumerability in the Difference Hierarchy.Marat Arslanov, Geoffrey Laforte & Theodore Slaman - 1998 - Journal of Symbolic Logic 63 (2):411-420.
    We show that the intersection of the class of 2-REA degrees with that of the $\omega$-r.e. degrees consists precisely of the class of d.r.e. degrees. We also include some applications and show that there is no natural generalization of this result to higher levels of the REA hierarchy.
     
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