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A random set which only computes strongly jump-traceable c.e. sets

Published online by Cambridge University Press:  12 March 2014

Noam Greenberg
Noam Greenberg*
Affiliation:
School of Mathematics, Statistics and Operations Research, Victoria University of Wellington, Wellington, New Zealand, E-mail: greenberg@msor.vuw.ac.nz
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Abstract

We prove that there is a , 1-random set Y such that every computably enumerable set which is computable from Y is strongly jump-traceable.

We also show that for every order function h there is an ω-c.e. random set Y such that every computably enumerable set which is computable from Y is h-jump-traceable. This establishes a correspondence between rates of jump-traceability and computability from ω-c.e. random sets.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 2 , June 2011 , pp. 700 - 718
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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