Splitting and nonsplitting, II: A $low_2$ C.e. Degree above which 0' is not splittable

Journal of Symbolic Logic 67 (4):1391-1430 (2002)
Abstract
It is shown that there exists a low2 Harrington non-splitting base-that is, a low2 computably enumerable (c.e.) degree a such that for any c.e. degrees x, y, if $0' = x \vee y$ , then either $0' = x \vee a$ or $0' = y \vee a$ . Contrary to prior expectations, the standard Harrington non-splitting construction is incompatible with the $low_{2}-ness$ requirements to be satisfied, and the proof given involves new techniques with potentially wider application
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DOI 10.2178/jsl/1190150292
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References found in this work BETA
Working Below a Low2 Recursively Enumerably Degree.Richard A. Shore & Theodore A. Slaman - 1990 - Archive for Mathematical Logic 29 (3):201-211.
Properly Σ2 Enumeration Degrees.S. B. Cooper & C. S. Copestake - 1988 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 34 (6):491-522.
Properly Σ2 Enumeration Degrees.S. B. Cooper & C. S. Copestake - 1988 - Mathematical Logic Quarterly 34 (6):491-522.
On the Distribution of Lachlan Nonsplitting Bases.S. Barry Cooper, Angsheng Li & Xiaoding Yi - 2002 - Archive for Mathematical Logic 41 (5):455-482.

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