An incomplete set of shortest descriptions

Journal of Symbolic Logic 77 (1):291-307 (2012)
Abstract
The truth-table degree of the set of shortest programs remains an outstanding problem in recursion theory. We examine two related sets, the set of shortest descriptions and the set of domain-random strings, and show that the truth-table degrees of these sets depend on the underlying acceptable numbering. We achieve some additional properties for the truth-table incomplete versions of these sets, namely retraceability and approximability. We give priority-free constructions of bounded truth-table chains and bounded truth-table antichains inside the truth-table complete degree by identifying an acceptable set of domain-random strings within each degree
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DOI 10.2178/jsl/1327068704
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References found in this work BETA
A Guided Tour of Minimal Indices and Shortest Descriptions.Marcus Schaefer - 1998 - Archive for Mathematical Logic 37 (8):521-548.
On Btt-Degrees of Sets of Minimal Numbers in Gödel Numberings.Jefim Kinber - 1977 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 23 (13-15):201-212.
Bounded Immunity and Btt‐Reductions.Stephen Fenner & Marcus Schaefer - 1999 - Mathematical Logic Quarterly 45 (1):3-21.
Immunity and Hyperimmunity for Sets of Minimal Indices.Frank Stephan & Jason Teutsch - 2008 - Notre Dame Journal of Formal Logic 49 (2):107-125.
On the Turing Degrees of Minimal Index Sets.Jason Teutsch - 2007 - Annals of Pure and Applied Logic 148 (1):63-80.

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