Geodesic
$CEA$ operators and the Ershov hierarchy
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2021), pp. 72-79

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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. 
@article{IVM_2021_8_a7,
     author = {M. M. Arslanov and I. I. Batyrshin and M. M. Yamaleev},
     title = {$CEA$ operators and the {Ershov} hierarchy},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {72--79},
     publisher = {mathdoc},
     number = {8},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_8_a7/}
}
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M. M. Arslanov; I. I. Batyrshin; M. M. Yamaleev. $CEA$ operators and the Ershov hierarchy. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2021), pp. 72-79. http://geodesic.mathdoc.fr/item/IVM_2021_8_a7/