Notre Dame Journal of Formal Logic

Effective Packing Dimension and Traceability

Rod Downey and Keng Meng Ng

Abstract

We study the Turing degrees which contain a real of effective packing dimension one. Downey and Greenberg showed that a c.e. degree has effective packing dimension one if and only if it is not c.e. traceable. In this paper, we show that this characterization fails in general. We construct a real A T ′′ which is hyperimmune-free and not c.e. traceable such that every real α T A has effective packing dimension 0. We construct a real B T which is not c.e. traceable such that every real α T B has effective packing dimension 0.

Article information

Source
Notre Dame J. Formal Logic, Volume 51, Number 2 (2010), 279-290.

Dates
First available in Project Euclid: 11 June 2010

Permanent link to this document
https://projecteuclid.org/euclid.ndjfl/1276284787

Digital Object Identifier
doi:10.1215/00294527-2010-017

Mathematical Reviews number (MathSciNet)
MR2667937

Zentralblatt MATH identifier
1204.03042

Subjects
Primary: 03D32: Algorithmic randomness and dimension [See also 68Q30]

Keywords
effective dimension Turing degrees

Citation

Downey, Rod; Ng, Keng Meng. Effective Packing Dimension and Traceability. Notre Dame J. Formal Logic 51 (2010), no. 2, 279--290. doi:10.1215/00294527-2010-017. https://projecteuclid.org/euclid.ndjfl/1276284787


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