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There is No Low Maximal D.C.E. Degree
Mathematical Logic Quarterly 46 (3):409-416 (2000)
Abstract
We show that for any computably enumerable set A and any equation image set L, if L is low and equation image, then there is a c.e. splitting equation image such that equation image. In Particular, if L is low and n-c.e., then equation image is n-c.e. and hence there is no low maximal n-c.e. degree.Author's Profile
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Citations of this work
There Are No Maximal Low D.C.E. Degrees.Liang Yu & Rod Downey - 2004 - Notre Dame Journal of Formal Logic 45 (3):147-159.
Splitting and nonsplitting II: A low {\sb 2$} C.E. degree about which ${\bf 0}'$ is not splittable.S. Barry Cooper & Angsheng Li - 2002 - Journal of Symbolic Logic 67 (4):1391-1430.
There is no low maximal d. c. e. degree– Corrigendum.Marat Arslanov, S. Barry Cooper & Angsheng Li - 2004 - Mathematical Logic Quarterly 50 (6):628-636.
References found in this work
The d.r.e. degrees are not dense.S. Cooper, Leo Harrington, Alistair Lachlan, Steffen Lempp & Robert Soare - 1991 - Annals of Pure and Applied Logic 55 (2):125-151.
The density of the low2 n-r.e. degrees.S. Barry Cooper - 1991 - Archive for Mathematical Logic 31 (1):19-24.
The discontinuity of splitting in the recursively enumerable degrees.S. Barry Cooper & Xiaoding Yi - 1995 - Archive for Mathematical Logic 34 (4):247-256.
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