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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Effective packing dimension of $ \Pi^0_1$-classes


Author: Chris J. Conidis
Journal: Proc. Amer. Math. Soc. 136 (2008), 3655-3662
MSC (2000): Primary 03Dxx, 68Qxx
Published electronically: May 15, 2008
MathSciNet review: 2415051
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Abstract: We construct a $ \Pi^0_1$-class $ X$ that has classical packing dimension 0 and effective packing dimension 1. This implies that, unlike in the case of effective Hausdorff dimension, there is no natural correspondence principle (as defined by Lutz) for effective packing dimension. We also examine the relationship between upper box dimension and packing dimension for $ \Pi^0_1$-classes.


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Additional Information

Chris J. Conidis
Affiliation: Department of Mathematics, The University of Chicago, 5734 University Avenue, Chicago, Illinois 60637-1546
Email: conidis@math.uchicago.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09335-0
PII: S 0002-9939(08)09335-0
Received by editor(s): August 2, 2007
Received by editor(s) in revised form: August 22, 2007
Published electronically: May 15, 2008
Additional Notes: The author would like to acknowledge the helpful input he received from Jan Reimann, as well as his thesis advisors, Robert I. Soare and Denis R. Hirschfeldt. The author would also like to thank the American Institute of Mathematics for hosting a valuable workshop in effective randomness which lead to the publication of this article.
Communicated by: Julia Knight
Article copyright: © Copyright 2008 American Mathematical Society