Post's Programme for the Ershov Hierarchy

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Post's Programme for the Ershov Hierarchy
This paper extends Post’s programme to finite levels of the Ershov hierarchy of ∆2 sets. Our initial characterisation, in the spirit of Post [27], 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 characterising 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 characterisation of n-enumerable degre...
Bahareh Afshari, George Barmpalias, S. Barry Coope
Added 16 Dec 2010
Updated 16 Dec 2010
Type Journal
Year 2007
Authors Bahareh Afshari, George Barmpalias, S. Barry Cooper, Frank Stephan
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