Article contents
Splitting and nonsplitting, II: A low2 c.e. degree above which 0′ is not splittable
Published online by Cambridge University Press: 12 March 2014
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
- Copyright
- Copyright © Association for Symbolic Logic 2002
References
REFERENCES
- 6
- Cited by