descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Apr 2010Publisher:Duke University PressJournal:Notre Dame Journal of Formal Logic, volume 51 (issn: 0029-4527,

Authors: Downey, Rod; Ng, Keng Meng;

doi: 10.1215/00294527-2010-017

Effective Packing Dimension and Traceability

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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.

Related Organizations

Victoria University of Wellington
New Zealand
Lincoln University - Pennsylvania
United States

Keywords

effective dimension, Turing degrees, 03D32

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