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June 2012 A real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one
Chris J. Conidis
J. Symbolic Logic 77(2): 447-474 (June 2012). DOI: 10.2178/jsl/1333566632

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).

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Chris J. Conidis. "A real of strictly positive effective packing dimension that does not compute a real of effective packing dimension one." J. Symbolic Logic 77 (2) 447 - 474, June 2012. https://doi.org/10.2178/jsl/1333566632

Information

Published: June 2012
First available in Project Euclid: 4 April 2012

zbMATH: 1251.03047
MathSciNet: MR2963016
Digital Object Identifier: 10.2178/jsl/1333566632

Subjects:
Primary: 03D32
Secondary: 68Q30

Rights: Copyright © 2012 Association for Symbolic Logic

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Vol.77 • No. 2 • June 2012
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