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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, Number 8, Pages 72–79
DOI: https://doi.org/10.26907/0021-3446-2021-8-72-79
(Mi ivm9705)
 

Brief communications

$CEA$ operators and the Ershov hierarchy

M. M. Arslanov, I. I. Batyrshin, M. M. Yamaleev

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
References:
Abstract: We examine the relationship between the $CEA$ hierarchy and the Ershov hierarchy within $\Delta_2^0$ Turing degrees. We study the long-standing problem raised in [1] about the existence of a low computably enumerable (c.e.) degree $\mathbf{a}$ for which the class of all non-c.e. $CEA(\mathbf{a})$ degrees does not contain $2$-c.e. degrees. We solve the problem by proving a stronger result: there exists a noncomputable low c.e. degree $\mathbf{a}$ such that any $CEA(\mathbf{a})$ $\omega$-c.e. degree is c.e. Also we discuss related questions and possible generalizations of this result.
Keywords: relative enumerability, computably enumerable set, Ershov's hierarchy, low degree.
Received: 18.06.2021
Revised: 18.06.2021
Accepted: 29.06.2021
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2021, Volume 65, Issue 8, Pages 63–69
DOI: https://doi.org/10.3103/S1066369X21080089
Document Type: Article
UDC: 510.535
Language: Russian
Citation: M. M. Arslanov, I. I. Batyrshin, M. M. Yamaleev, “$CEA$ operators and the Ershov hierarchy”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 8, 72–79; Russian Math. (Iz. VUZ), 65:8 (2021), 63–69
Citation in format AMSBIB
\Bibitem{ArsBatYam21}
\by M.~M.~Arslanov, I.~I.~Batyrshin, M.~M.~Yamaleev
\paper $CEA$ operators and the Ershov hierarchy
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2021
\issue 8
\pages 72--79
\mathnet{http://mi.mathnet.ru/ivm9705}
\crossref{https://doi.org/10.26907/0021-3446-2021-8-72-79}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2021
\vol 65
\issue 8
\pages 63--69
\crossref{https://doi.org/10.3103/S1066369X21080089}
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    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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