Geodesic
Nonuniformity of downwards density in the $n$-computably enumerable Turing degrees
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2022), pp. 124-131 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 
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     title = {Nonuniformity of downwards density in the $n$-computably enumerable {Turing} degrees},
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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/

[1] Soar R. I., Vychislimo perechislimye mnozhestva i stepeni, per. s angl., ed. Arslanov M. M., Kazansk. matem. ob-vo, Kazan, 2000 | MR

[2] Downey R., Stob M., “Splitting theorems in recursion theory”, Ann. Pure and Appl. Logic, 65:1 (1993), 1–106 | DOI | MR

[3] Rodzhers Kh., Teoriya rekursivnykh funktsii i effektivnaya vychislimost, per. s angl., ed. Uspenskii V. A., Mir, M., 1972 | MR

[4] Cooper B., Li A., “Non-Uniformity and Generalised Sacks Splitting”, Acta Math. Sinica, 18:2 (2002), 327–334 | DOI | MR

[5] Arslanov M. M., Kalimullin I.Sh., Lempp S., “On Downey's conjecture”, J. Symbolic Logic, 75:2 (2010), 401–441 | DOI | MR