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Splitting and nonsplitting, II: A low2 c.e. degree above which 0′ is not splittable

Published online by Cambridge University Press:  12 March 2014

S. Barry Cooper  and
Angsheng Li
S. Barry Cooper
Affiliation:
School of Mathematics, University of Leeds, Leeds, LS2 9JT, England, E-mail: s.b.cooper@leeds.ac.uk, URL: http://www.amsta.leeds.ac.uk/~pmt6sbc
Angsheng Li*
Affiliation:
School of Mathematics, University of Leeds, Leeds, LS2 9JT, England, E-mail: angsheng@amsta.leeds.ac.uk
*
Institute of Software, Chinese Academy of Sciences, P.O. Box, 8718, Beijing, 100080, P.R. of, China, E-mail: angsheng@ios.ac.cn
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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 ∨ y, then either 0′ = x ∨ a or 0′ = y ∨ a. Contrary to prior expectations, the standard Harrington non-splitting construction is incompatible with the low2-ness requirements to be satisfied, and the proof given involves new techniques with potentially wider application.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 4 , December 2002 , pp. 1391 - 1430
Copyright
Copyright © Association for Symbolic Logic 2002

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References

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