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Diagonally Non-Computable Functions and Bi-Immunity

Published online by Cambridge University Press:  12 March 2014

Carl G. Jockusch Jr.  and
Andrew E. M. Lewis
Carl G. Jockusch Jr.
Affiliation:
University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801-2975, USA, E-mail: jockusch@math.uiuc.edu, URL: http://www.math.uiuc.edu/~jockusch/
Andrew E. M. Lewis
Affiliation:
School of Mathematics, University of Leeds, Leeds, LS2 9JT, UK, E-mail: andy@aemlewis.co.uk, URL: http://aemlewis.co.uk/
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Abstract

We prove that every diagonally noncomputable function computes a set A which is bi-immune, meaning that neither A nor its complement has an infinite computably enumerable subset.

Keywords

03D28
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 78 , Issue 3 , September 2013 , pp. 977 - 988
Copyright
Copyright © Association for Symbolic Logic 2013

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References

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