Mustafa, M.Sorbi, Andrea2015-12-252015-12-252012Mustafa Manat, Sorbi Andrea; 2012; Positive undecidable numberings in the Ershov hierarchyhttp://nur.nu.edu.kz/handle/123456789/971We 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.enResearch Subject Categories::MATHEMATICSnumberingArticle