Notre Dame Journal of Formal Logic

Effective Packing Dimension and Traceability

Rod Downey and Keng Meng Ng


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.

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

First available in Project Euclid: 11 June 2010

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

effective dimension Turing degrees


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.

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