Faizrakhmanov, M. Kh. Turing jumps in the Ershov hierarchy. (English. Russian original) Zbl 1287.03094 Algebra Logic 50, No. 3, 279-289 (2011); translation from Algebra Logika 50, No. 3, 399-414 (2011). In this paper the authors study infinite levels of the Ershov difference hierarchy which are proper for Turing jumps of degrees. It is proved that if a set \(A\) and an ordinal \(\alpha<\omega^{\omega}\) such that \(A'\in\Pi^{-1}_{\alpha}\), then \(A'\in\Delta^{-1}_{\alpha}\), if \(A'\in\Sigma^{-1}_{\omega^n}\), \(n>0\), then \(A'\in\Delta^{-1}_{\omega^n}\), if \(A'\in\Sigma^{-1}_{\omega^nm}\) for some \(m,n>0\), then \(A'\in\Delta^{-1}_{\omega^n}\), and for every \(n>0\) there exists a set \(A\) such that \(A'\in\Delta^{-1}_{\omega^{n+1}}-\Delta^{-1}_{\omega^{n}}\). Reviewer: Marat M. Arslanov (Kazan) Cited in 2 Documents MSC: 03D55 Hierarchies of computability and definability 03D28 Other Turing degree structures Keywords:Turing jumps; Ershov hierarchy; constructive ordinals; superlow sets × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Yu. L. Ershov, ”On a hierarchy of sets I,” Algebra Logika, 7, No. 1, 47–73 (1968). · Zbl 0216.00901 [2] Yu. L. Ershov, ”On a hierarchy of sets II,” Algebra Logika, 7, No. 4, 15–47 (1968). · Zbl 0216.00902 [3] Yu. L. Ershov, ”On a hierarchy of sets III,” Algebra Logika, 9, No. 1, 34–51 (1970). [4] M. M. Arslanov, The Ershov Hierarchy, A Special Course in Mathematics, Kazan State Univ., Kazan (2007). · Zbl 1279.03067 [5] H. G. Carstens, ” $ \(\backslash\)Delta_2\^0 $ -Mengen,” Arch. Math. Logik Grundl., 18, 55–65 (1976). · Zbl 0356.02039 · doi:10.1007/BF02007257 [6] B. Schaeffer, ”Dynamic notions of genericity and array noncomputability,” Ann. Pure Appl. Log., 95, Nos. 1–3, 37–69 (1998). · Zbl 0932.03048 · doi:10.1016/S0168-0072(98)00014-1 [7] S. Walk, ”Towards a definition of the array computable degrees,” Ph. D. Thesis, Univ. Notre Dame (1999). [8] I. Sh. Kalimullin, ”Some notes on degree spectra of the structures,” Lect. Notes Comput. Sci., 4497, Springer-Verlag, Berlin (2007), pp. 389–397. · Zbl 1151.03330 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.