Geodesic
Nonuniformity of downwards density in the $n$-computably enumerable Turing degrees
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2022), pp. 124-131

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In 1993 R. Downey and M. Stob showed that downwards density of computably enumerable (further, c.e.) Turing degrees in the partial order of $2$-c.e. Turing degrees cannot be proved by a uniform construction. In this paper their result is generalized for any $n > 2$ and it is shown that there is no a uniform consruction for the downwards denstiy of $(n-1)$-c.e. degrees in the structure of $n$-c.e. degrees. Moreover, it is shown that there is no a uniform construction for the downwards denstiy in the structure of $n$-c.e. degrees.
Keywords: Turing degree, the Ershov hierarchy, downwards density.
Mots-clés : uniform construction 
@article{IVM_2022_11_a8,
     author = {A. I. Talipova and M. M. Yamaleev},
     title = {Nonuniformity of downwards density in the $n$-computably enumerable {Turing} degrees},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {124--131},
     publisher = {mathdoc},
     number = {11},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_11_a8/}
}
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A. I. Talipova; M. M. Yamaleev. Nonuniformity of downwards density in the $n$-computably enumerable Turing degrees. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2022), pp. 124-131. http://geodesic.mathdoc.fr/item/IVM_2022_11_a8/