Show simple item record Melnikov A.G. Selivanov V.L. Yamaleev M.M. 2021-02-25T20:34:04Z 2021-02-25T20:34:04Z 2020
dc.identifier.issn 0168-0072
dc.description.abstract © 2019 Elsevier B.V. In the late 1980s, Selivanov used typed Boolean combinations of arithmetical sets to extend the Ershov hierarchy beyond Δ20 sets. Similar to the Ershov hierarchy, Selivanov's fine hierarchy {Σγ}γ<ε0 proceeds through transfinite levels below ε0 to cover all arithmetical sets. In this paper we use a 0‴ construction to show that the Σ30 Turing degrees are properly contained in the Σωω+2 Turing degrees (to be defined); intuitively, the latter class consists of “non-uniformly Σ30 sets” in the sense that will be clarified in the introduction. The question whether the hierarchy was proper at this level with respect to Turing reducibility remained open for over 20 years.
dc.relation.ispartofseries Annals of Pure and Applied Logic
dc.subject Arithmetical hierarchy
dc.subject Ershov hierarchy
dc.subject Fine hierarchy
dc.subject Turing degree
dc.title Turing reducibility in the fine hierarchy
dc.type Article
dc.relation.ispartofseries-issue 7
dc.relation.ispartofseries-volume 171
dc.collection Публикации сотрудников КФУ SCOPUS01680072-2020-171-7-SID85085152188

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  • Публикации сотрудников КФУ Scopus [24551]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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