The Journal of Symbolic Logic

Research Article

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

Guohua Wu

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

Abstract.

In this paper, we study the bi-isolation phenomena in the d.c.e. degrees and prove that there are c.e. degrees c 1 < c 2 and a d.c.e. degree d ∈ (c 1, c 2) such that (c 1, d) and (d, c 2) contain no c.e. degrees. Thus, the c.e. degrees between c 1 and c 2 are all incomparable with d. We also show that there are d.c.e. degrees d 1 < d 2 such that (d 1, d 2) contains a unique c.e. degree.

(Received June 13 2002)

(Accepted December 21 2003)