Geodesic
Turing computability: structural theory
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Seminar on Algebra and Mathematical Logic of the Kazan (Volga Region) Federal University, Tome 157 (2018), pp. 8-41

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In this work, we review results of the last years related to the development of the structural theory of $n$-c.e. Turing degrees for $n>1$. We also discuss possible approaches to solution of the open problems.
Keywords: computably enumerable set, Turing degree, Ershov's hierarchy, definability. 
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     author = {M. M. Arslanov and M. M. Yamaleev},
     title = {Turing computability: structural theory},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {8--41},
     publisher = {mathdoc},
     volume = {157},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_157_a1/}
}
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M. M. Arslanov; M. M. Yamaleev. Turing computability: structural theory. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Seminar on Algebra and Mathematical Logic of the Kazan (Volga Region) Federal University, Tome 157 (2018), pp. 8-41. http://geodesic.mathdoc.fr/item/INTO_2018_157_a1/