Geodesic
Turing degrees in refinements of the arithmetical hierarchy
Algebra i logika, Tome 57 (2018) no. 3, pp. 338-361

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We investigate the problem of characterizing proper levels of the fine hierarchy (up to Turing equivalence). It is known that the fine hierarchy exhausts arithmetical sets and contains as a small fragment finite levels of Ershov hierarchies (relativized to $\varnothing^n$, $n\omega$), which are known to be proper. Our main result is finding a least new (i.e., distinct from the levels of the relativized Ershov hierarchies) proper level. We also show that not all new levels are proper.
Keywords: Ershov hierarchy, fine hierarchy, arithmetical hierarchy, Turing degrees. 
@article{AL_2018_57_3_a5,
     author = {V. L. Selivanov and M. M. Yamaleev},
     title = {Turing degrees in refinements of the arithmetical hierarchy},
     journal = {Algebra i logika},
     pages = {338--361},
     publisher = {mathdoc},
     volume = {57},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2018_57_3_a5/}
}
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V. L. Selivanov; M. M. Yamaleev. Turing degrees in refinements of the arithmetical hierarchy. Algebra i logika, Tome 57 (2018) no. 3, pp. 338-361. http://geodesic.mathdoc.fr/item/AL_2018_57_3_a5/