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Bi-isolation in the d.c.e. degrees

Published online by Cambridge University Press:  12 March 2014

Guohua Wu
Guohua Wu*
Affiliation:
School of Mathematical and Computing Sciences, Victoria University of Wellington, P. O. BOX 600, Wellington, New Zealand, E-mail: wu@mcs.vuw.ac.nz
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 69 , Issue 2 , June 2004 , pp. 409 - 420
Copyright
Copyright © Association for Symbolic Logic 2004

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