Geodesic
Definable relations in structures of Turing degrees
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2014), pp. 77-81

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In this paper we investigate questions about the definability of classes of $n$-computably enumerable (c.e.) sets and degrees in the Ershov difference hierarchy. It is proved that the class of all c.e. sets it is definable under the set inclusion $\subseteq$ in all finite levels of the difference hierarchy. It is also proved the definability of all $m$-c.e. degrees in each higher level of the hierarchy. Besides, for each level $n$, $n\ge2$, of the hierarchy a definable non-trivial subset of $n$-c.e. degrees is established.
Keywords: computably enumerable sets, Turing degrees of unsolvability, high degrees, major subsets.
Mots-clés : definable relations 
@article{IVM_2014_2_a10,
     author = {M. M. Arslanov},
     title = {Definable relations in structures of {Turing} degrees},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {77--81},
     publisher = {mathdoc},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_2_a10/}
}
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M. M. Arslanov. Definable relations in structures of Turing degrees. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2014), pp. 77-81. http://geodesic.mathdoc.fr/item/IVM_2014_2_a10/