Rogers semilattices of families of two embedded sets in the Ershov hierarchy

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dc.contributor.authorBadaev, Serikzhan A.
dc.contributor.authorMustafa, M.
dc.date.accessioned2015-12-25T05:41:04Z
dc.date.available2015-12-25T05:41:04Z
dc.date.issued2012
dc.description.abstractLet a be a Kleene's ordinal notation of a nonzero computable ordinal. We give a su cient condition on a, so that for every 􀀀1 a {computable family of two embedded sets, i.e. two sets A;B, with A properly contined in B, the Rogers semilattice of the family is in nite. This condition is satis ed by every notation of !; moreover every nonzero computable ordinal that is not sum of any two smaller ordinals has a notation that satis es this condition. On the other hand, we also give a su cient condition on a, that yields that there is a 􀀀1 a {computable family of two embedded sets, whose Rogers semilattice consists of exactly one element; this condition is satis ed by all notations of every successor ordinal bigger than 1, and by all notations of the ordinal !+!; moreover every computable ordinal that is sum of two smaller ordinals has a notation that satis es this condition. We also show that for every nonzero n 2 !, or n = !, and every notation of a nonzero ordinal there exists a 􀀀1 a {computable family of cardinality n, whose Rogers semilattice consists of exactly one element.ru_RU
dc.identifier.citationBadaev Serikzhan A., Mustafa M.; 2012; Rogers semilattices of families of two embedded sets in the Ershov hierarchyru_RU
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/972
dc.language.isoenru_RU
dc.subjectResearch Subject Categories::MATHEMATICSru_RU
dc.subjectErshov hierarchyru_RU
dc.titleRogers semilattices of families of two embedded sets in the Ershov hierarchyru_RU
dc.typeArticleru_RU

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