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AVOIDING EFFECTIVE PACKING DIMENSION 1 BELOW ARRAY NONCOMPUTABLE C.E. DEGREES

Published online by Cambridge University Press:  01 August 2018

ROD DOWNEY  and
JONATHAN STEPHENSON
ROD DOWNEY
Affiliation:
DEPARTMENT OF MATHEMATICS, STATISTICS, AND OPERATIONS RESEARCH VICTORIA UNIVERSITY OF WELLINGTON P.O. BOX 600 WELLINGTON, NEW ZEALANDE-mail:rod.downey@msor.vuw.ac.nz
JONATHAN STEPHENSON
Affiliation:
MATHEMATICS AND STATISTICS VALPARAISO UNIVERSITY GELLERSEN CENTER, ROOM 112 1900 CHAPEL DRIVE VALPARAISO, IN46383, USAE-mail:jonny.stephenson@valpo.edu
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Abstract

Recent work of Conidis [3] shows that there is a Turing degree with nonzero effective packing dimension, but which does not contain any set of effective packing dimension 1.

This article shows the existence of such a degree below every c.e. array noncomputable degree, and hence that they occur below precisely those of the c.e. degrees which are array noncomputable.

Keywords

03D3268Q30Kolmogorov complexityeffective packing dimensionarray noncomputability
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 2 , June 2018 , pp. 717 - 739
Copyright
Copyright © The Association for Symbolic Logic 2018 

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