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Erschienen in:
2003 | OriginalPaper | Buchkapitel
Completeness and Universality of Arithmetical Numberings
verfasst von : Serikzhan Badaev, Sergey Goncharov, Andrea Sorbi
Erschienen in: Computability and Models
Verlag: Springer US
Enthalten in: Professional Book Archive
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We investigate completeness and universality notions, relative to different oracles, and the interconnection between these notions, with applications to arithmetical numberings. We prove that principal numberings are complete; completeness is independent of the oracle; the degree of any incomplete numbering is meet-reducible, uniformly complete numberings exist. We completely characterize which finite arithmetical families have a universal numbering.