Bi-Isolation in the D.C.E. Degrees

Journal of Symbolic Logic 69 (2):409 - 420 (2004)
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Abstract

In this paper, we study the bi-isolation phenomena in the d.c.e. degrees and prove that there are c.e. degrees c₁ < c₂ and a d.c.e. degree d ∈ (c₁, c₂) such that (c₁, d) and (d, c₂) contain no c.e. degrees. Thus, the c.e. degrees between c₁ and c₂ are all incomparable with d. We also show that there are d.c.e. degrees d₁ < d₂ such that (d₁, d₂) contains a unique c.e. degree

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Citations of this work

Intervals containing exactly one c.e. degree.Guohua Wu - 2007 - Annals of Pure and Applied Logic 146 (1):91-102.

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References found in this work

The Isolated D. R. E. Degrees are Dense in the R. E. Degrees.Geoffrey Laforte - 1996 - Mathematical Logic Quarterly 42 (1):83-103.
Isolation and the high/low hierarchy.Shamil Ishmukhametov & Guohua Wu - 2002 - Archive for Mathematical Logic 41 (3):259-266.
The density of the low2 n-r.e. degrees.S. Barry Cooper - 1991 - Archive for Mathematical Logic 31 (1):19-24.
Isolation and the Jump Operator.Guohua Wu - 2001 - Mathematical Logic Quarterly 47 (4):525-534.

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