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

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

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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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.
The Density of the Low2 N-R.E. Degrees.S. Barry Cooper - 1991 - Archive for Mathematical Logic 31 (1):19-24.
Isolation and the High/Low Hierarchy.Shamil Ishmukhametov & Guohua Wu - 2002 - Archive for Mathematical Logic 41 (3):259-266.
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.

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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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