Geodesic
Arithmetical level of a~class of superhigh sets
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2014), pp. 53-58.

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We find the proper arithmetical level of the class of superhigh sets.
Keywords: superhigh set, arithmetical hierarchy, arithmetical class. 
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M. Kh. Faizrakhmanov. Arithmetical level of a~class of superhigh sets. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2014), pp. 53-58. http://geodesic.mathdoc.fr/item/IVM_2014_5_a4/

[1] Mohrherr J., “A refinement of low$_n$ and high$_n$ for the r.e. degrees”, Z. Math. Logik Grundlag. Math., 32:1 (1986), 5–12 | DOI | MR | Zbl

[2] Kjos-Hanssen B., Nies A., “Superhighness”, Notre Dame J. Formal Logic, 50:4 (2009), 445–452 | DOI | MR | Zbl

[3] Nies A., Computability and randomness, Oxford University Press, 2009 | MR | Zbl

[4] Dobrinen N. L., Simpson S. G., “Almost everywhere domination”, J. Symbolic Logic, 69:3 (2004), 914–922 | DOI | MR | Zbl

[5] Cholak P., Downey R., Greenberg N., “Strong jump-traceabilty. I: The computably enumerable case”, Adv. Math., 217:5 (2008), 2045–2074 | DOI | MR | Zbl

[6] Ishmukhametov S., “Weak recursive degrees and a problem of Spector”, Recursion theory and complexity (Kazan, 1997), de Gruyter Ser. Log. Appl., 2, de Gruyter, Berlin, 1999, 81–87 | MR | Zbl

[7] Nies A., Greenberg N., Hirschfeldt D., “Characterizing the strongly jump-traceable sets via randomness”, Adv. Math., 231:3–4 (2012), 2252–2293 | MR | Zbl

[8] Soar R. I., Vychislimo perechislimye mnozhestva i stepeni, Kazansk. matem. o-vo, Kazan, 2000 | MR | Zbl

[9] Faizrakhmanov M. Kh., “O polureshetke, porozhdennoi supernizkimi vychislimo perechislimymi stepenyami”, Izv. vuzov. Matem., 2011, no. 1, 85–90 | MR | Zbl

[10] Nies A., “Reals which compute little”, Logic Colloquium 2002, Lecture Notes in Logic, 27, La Jolla, CA, 2006, 260–274 | MR

[11] Faizrakhmanov M. Kh., “Vychislimye numeratsii semeistv nizkikh mnozhestv i tyuringovy skachki v ierarkhii Ershova”, Sib. matem. zhurn., 51:6 (2010), 1435–1439 | MR