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Nonisolated degrees and the jump operator

Annals of Pure and Applied Logic 117 (1-3):209-221 (2002)

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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.details 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. Download Export citation Bookmark 6 citations
Isolation and the Jump Operator.Guohua Wu - 2001 - Mathematical Logic Quarterly 47 (4):525-534.details We show the existence of a high d. c. e. degree d and a low2 c.e. degree a such that d is isolated by a. Download Export citation Bookmark 6 citations
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
The d.r.e. degrees are not dense.S. Barry Cooper, Leo Harrington, Alistair H. Lachlan, Steffen Lempp & Robert I. Soare - 1991 - Annals of Pure and Applied Logic 55 (2):125-151.details By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees. Download Export citation Bookmark 31 citations
The Isolated D. R. E. Degrees are Dense in the R. E. Degrees.Geoffrey Laforte - 1996 - Mathematical Logic Quarterly 42 (1):83-103.details In the present paper we prove that the isolated differences of r. e. degrees are dense in the r. e. degrees. Download Export citation Bookmark 13 citations
The d.r.e. degrees are not dense.S. Cooper, Leo Harrington, Alistair Lachlan, Steffen Lempp & Robert Soare - 1991 - Annals of Pure and Applied Logic 55 (2):125-151.details By constructing a maximal incomplete d.r.e. degree, the nondensity of the partial order of the d.r.e. degrees is established. An easy modification yields the nondensity of the n-r.e. degrees and of the ω-r.e. degrees. Download Export citation Bookmark 24 citations
Gerald E. Sacks. The recursively enumerable degrees are dense. Annals of mathematics, ser. 2 vol. 80 (1964), pp. 300–312. [REVIEW]Gerald E. Sacks - 1969 - Journal of Symbolic Logic 34 (2):294-295.details Download Export citation Bookmark 38 citations
Isolated d.r.e. degrees are dense in r.e. degree structure.Decheng Ding & Lei Qian - 1996 - Archive for Mathematical Logic 36 (1):1-10.details Download Export citation Bookmark 6 citations

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