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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Branching degrees above low degrees


Author: Peter A. Fejer
Journal: Trans. Amer. Math. Soc. 273 (1982), 157-180
MSC: Primary 03D25; Secondary 03D30
MathSciNet review: 664035
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Abstract: In this paper, we investigate the location of the branching degrees within the recursively enumerable (r.e.) degrees. We show that there is a branching degree below any given nonzero r.e. degree and, using a new branching degree construction and a technique of Robinson, that there is a branching degree above any given low r.e. degree. Our results extend work of Shoenfield and Soare and Lachlan on the generalized nondiamond question and show that the branching degrees form an automorphism base for the r.e. degrees.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0664035-X
PII: S 0002-9947(1982)0664035-X
Keywords: Recursively enumerable degree, branching degree, low degree, generalized nondiamond question, automorphism base
Article copyright: © Copyright 1982 American Mathematical Society