Geodesic
Turing jumps in the Ershov hierarchy
Algebra i logika, Tome 50 (2011) no. 3, pp. 399-414

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We look at infinite levels of the Ershov hierarchy in the natural system of notation, which are proper for jumps of sets. It is proved that proper infinite levels for jumps are confined to $\Delta^{-1}_a$-levels, where $a$ stands for an ordinal $\omega^n>1$.
Keywords: Turing jumps, Ershov hierarchy, constructive ordinals, superlow sets. 
@article{AL_2011_50_3_a6,
     author = {M. Kh. Faizrakhmanov},
     title = {Turing jumps in the {Ershov} hierarchy},
     journal = {Algebra i logika},
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     volume = {50},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2011_50_3_a6/}
}
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M. Kh. Faizrakhmanov. Turing jumps in the Ershov hierarchy. Algebra i logika, Tome 50 (2011) no. 3, pp. 399-414. http://geodesic.mathdoc.fr/item/AL_2011_50_3_a6/