An incomplete set of shortest descriptions

Journal of Symbolic Logic 77 (1):291-307 (2012)
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
Jefim Kinber (1977). On Btt-Degrees of Sets of Minimal Numbers in Gödel Numberings. Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 23 (13-15):201-212.
Jason Teutsch (2007). On the Turing Degrees of Minimal Index Sets. Annals of Pure and Applied Logic 148 (1):63-80.

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