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A real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one

Published online by Cambridge University Press:  12 March 2014

Chris J. Conidis
Chris J. Conidis*
Affiliation:
Department of Pure Mathematics, University of Waterloo,Waterloo, ON N2L 3G1, Canada, E-mail: cconidis@math.uwaterloo.ca
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Abstract

Recently, the Dimension Problem for effective Hausdorff dimension was solved by J. Miller in [14], where the author constructs a Turing degree of non-integral Hausdorff dimension. In this article we settle the Dimension Problem for effective packing dimension by constructing a real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one (on the other hand, it is known via [10. 3. 7] that every real of strictly positive effective Hausdorff dimension computes reals whose effective packing dimensions are arbitrarily close to, but not necessarily equal to, one).

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 2 , June 2012 , pp. 447 - 474
Copyright
Copyright © Association for Symbolic Logic 2012

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References

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