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Bi-Isolation in the D.C.E. Degrees
The Journal of Symbolic Logic
Vol. 69, No. 2 (Jun., 2004), pp. 409-420
Published by: Association for Symbolic Logic
Stable URL: http://www.jstor.org/stable/30041734
Page Count: 12
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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.
The Journal of Symbolic Logic © 2004 Association for Symbolic Logic