Please use this identifier to cite or link to this item: https://doi.org/10.1093/logcom/exm032
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dc.titlePosts programme for the Ershov hierarchy
dc.contributor.authorAfshari, B.
dc.contributor.authorBarmpalias, G.
dc.contributor.authorCooper, S.B.
dc.contributor.authorStephan, F.
dc.date.accessioned2014-10-28T02:51:32Z
dc.date.available2014-10-28T02:51:32Z
dc.date.issued2007-12
dc.identifier.citationAfshari, B., Barmpalias, G., Cooper, S.B., Stephan, F. (2007-12). Posts programme for the Ershov hierarchy. Journal of Logic and Computation 17 (6) : 1025-1040. ScholarBank@NUS Repository. https://doi.org/10.1093/logcom/exm032
dc.identifier.issn0955792X
dc.identifier.urihttp://scholarbank.nus.edu.sg/handle/10635/104609
dc.description.abstractThis article extends Posts; programme to finite levels of the Ershov hierarchy of Δ2 sets. Our initial characterization, in the spirit of Post (1994, Bulletin of the American Mathematical Society, 50, 284316), of the degrees of the immune and hyperimmune n-enumerable sets leads to a number of results setting other immunity properties in the context of the Turing and wtt-degrees derived from the Ershov hierarchy. For instance, we show that any n-enumerable hyperhyperimmune set must be co-enumerable, for each n < 2. The situation with regard to the wtt-degrees is particularly interesting, as demonstrated by a range of results concerning the wtt-predecessors of hypersimple sets.Finally, we give a number of results directed at characterizing basic classes of n-enumerable degrees in terms of natural information content. For example, a 2-enumerable degree contains a 2-enumerable dense immune set iff it contains a 2-enumerable r-cohesive set iff it bounds a high enumerable set. This result is extended to a characterization of n-enumerable degrees which bound high enumerable degrees. Furthermore, a characterization for n-enumerable degrees bounding only low2 enumerable degrees is given.
dc.sourceScopus
dc.subjectCohesiveness
dc.subjectEnumerable sets
dc.subjectErshov hierarchy
dc.subjectImmunity properties
dc.subjectJump classes
dc.subjectPost's programme
dc.subjectTuring degrees
dc.typeConference Paper
dc.contributor.departmentMATHEMATICS
dc.description.doi10.1093/logcom/exm032
dc.description.sourcetitleJournal of Logic and Computation
dc.description.volume17
dc.description.issue6
dc.description.page1025-1040
dc.description.codenJLCOE
dc.identifier.isiut000252665100002
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