Classifying equivalence relations in the Ershov hierarchy

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dc.contributor.authorMustafa, Manat
dc.contributor.authorBazhenov, Nikolay
dc.contributor.authorMauro, Luca San
dc.contributor.authorSorbi, Andrea
dc.contributor.authorYamaleev, Mars
dc.date.accessioned2020-05-12T10:19:36Z
dc.date.available2020-05-12T10:19:36Z
dc.date.issued2020-02-13
dc.description.abstractComputably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility ⩽c. This gives rise to a rich degree structure. In this paper, we lift the study of c-degrees to the Δ02 case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree structure induced by ⩽c on the Σ−1a∖Π−1a equivalence relations. A special focus of our work is on the (non)existence of infima and suprema of c-degrees.en_US
dc.identifier.citationBazhenov, N., Mustafa, M., San Mauro, L., Sorbi, A., & Yamaleev, M. (2020). Classifying equivalence relations in the Ershov hierarchy. Archive for Mathematical Logic, 1-30.en_US
dc.identifier.urihttps://doi.org/10.1007/s00153-020-00710-1
dc.identifier.urihttp://nur.nu.edu.kz/handle/123456789/4660
dc.language.isoenen_US
dc.publisherSpringeren_US
dc.rightsAttribution-NonCommercial-ShareAlike 3.0 United States*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/us/*
dc.titleClassifying equivalence relations in the Ershov hierarchyen_US
dc.typeArticleen_US
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