Minimal pairs in initial segments of the recursively enumerable degrees

Minimal pairs in initial segments of the recursively enumerable degrees

We show that for every r.e. Turing degreea>0, there is an r.e. degreeb<a which is not half of a minimal pair in the initial segment [0, a].

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Bibliographic Details
Published in:Israel journal of mathematics Vol. 100; no. 1; pp. 7 - 27
Main Authors: Downey, R., Stob, M.
Format: Journal Article
Language:English
Published: Heidelberg Springer Nature B.V 01-01-1997
Subjects:
Mathematics
Segments
Online Access:Get full text
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Description
Summary:We show that for every r.e. Turing degreea>0, there is an r.e. degreeb<a which is not half of a minimal pair in the initial segment [0, a].
ISSN:0021-2172
1565-8511
DOI:10.1007/BF02773633