Positive undecidable numberings in the Ershov hierarchy

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dc.contributor.authorMustafa, M.
dc.contributor.authorSorbi, Andrea
dc.date.accessioned2015-12-25T05:34:30Z
dc.date.available2015-12-25T05:34:30Z
dc.date.issued2012
dc.description.abstractWe give a su cient condition for an in nite computable family of 􀀀1 a sets, to have computable positive but undecidable numberings, where a is a notation for a nonzero computable ordinal. This extends a theorem proved by Talasbaeva for the nite levels of the Ershov hierarchy. In par- ticular the family of all 􀀀1 a sets has positive undecidable numberings: this veri es for all levels of the Ershov hierarchy a conjecture due to Badaev and Goncharov. We point out also that for every ordinal notation a of a nonzero ordinal, there are families of 􀀀1 a sets having positive numberings, but no Friedberg numberings: this answers for all levels (whether nite or in nite) of the Ershov hierarchy, a question originally raised, only for the nite levels over level 1, by Badaev and Goncharov.ru_RU
dc.identifier.citationMustafa Manat, Sorbi Andrea; 2012; Positive undecidable numberings in the Ershov hierarchyru_RU
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/971
dc.language.isoenru_RU
dc.subjectResearch Subject Categories::MATHEMATICSru_RU
dc.subjectnumberingru_RU
dc.titlePositive undecidable numberings in the Ershov hierarchyru_RU
dc.typeArticleru_RU

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