Effective Packing Dimension and Traceability
Rodney G. Downey, Keng Meng Ng · Notre Dame Journal of Formal Logic · 2010
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.