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Published online by Cambridge University Press: 11 October 2006
We show that for any 2-computably enumerable Turing degree ${\bf l}$, any computably enumerable degree ${\bf a}$ and any Turing degree ${\bf s}$, if ${\bf l'=\boldsymbol{0}'}$, ${\bf l<a}$, ${\bf s\geq \boldsymbol{0}'}$, and ${\bf s}$ is c.e. in ${\bf a}$, then there is a 2-computably enumerable degree ${\bf x}$ with the following properties:
${\bf l<x<a}$; and
${\bf x'=s}$