2008 | OriginalPaper | Chapter
Extensions of Embeddings in the Computably Enumerable Degrees
Author : Jitai Zhao
Published in: Theory and Applications of Models of Computation
Publisher: Springer Berlin Heidelberg
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In this paper, we study the extensions of embeddings in the computably enumerable Turing degrees. We show that for any c.e. degrees
${\bf x\not\leq y}$
, if either
y
is low or
x
is high, then there is a c.e. degree
a
such that both
0 < a
≤ x
and
${\bf x\not\leq y\cup a}$
hold.