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This article is cited in 9 scientific papers (total in 9 papers)
The Rogers semilattices of generalized computable enumerations
M. Kh. Faizrahmanov Kazan (Volga Region) Federal University, Lobachevskiĭ Institute of Mathematics and Mechanics, Kazan, Russia
Abstract:
We study the cardinality and structural properties of the Rogers semilattice of generalized computable enumerations with arbitrary noncomputable oracles and oracles of hyperimmune Turing degree. We show the infinity of the Rogers semilattice of generalized computable enumerations of an arbitrary nontrivial family with a noncomputable oracle. In the case of oracles of hyperimmune degree we prove that the Rogers semilattice of an arbitrary infinite family includes an ideal without minimal elements and establish that the top, if present, is a limit element under the condition that the family contains the inclusion-least set.
Keywords:
computable enumeration, generalized computable enumeration, Rogers semilattice, hyperimmune set, minimal enumeration, universal enumeration.
Received: 16.11.2016
Citation:
M. Kh. Faizrahmanov, “The Rogers semilattices of generalized computable enumerations”, Sibirsk. Mat. Zh., 58:6 (2017), 1418–1427; Siberian Math. J., 58:6 (2017), 1104–1110
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https://www.mathnet.ru/eng/smj2948 https://www.mathnet.ru/eng/smj/v58/i6/p1418
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Abstract page: | 256 | Full-text PDF : | 80 | References: | 43 | First page: | 7 |
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