Notre Dame Journal of Formal Logic
- Notre Dame J. Formal Logic
- Volume 51, Number 2 (2010), 279-290.
Effective Packing Dimension and Traceability
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 which is hyperimmune-free and not c.e. traceable such that every real has effective packing dimension 0. We construct a real which is not c.e. traceable such that every real has effective packing dimension 0.
Notre Dame J. Formal Logic, Volume 51, Number 2 (2010), 279-290.
First available in Project Euclid: 11 June 2010
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03D32: Algorithmic randomness and dimension [See also 68Q30]
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