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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, Number 8, Pages 81–86
DOI: https://doi.org/10.26907/0021-3446-2020-8-81-86
(Mi ivm9606)
 

This article is cited in 2 scientific papers (total in 2 papers)

Brief communications

Isolation from side in $2$-computably enumerable degrees

M. M. Yamaleev

Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
Full-text PDF (321 kB) Citations (2)
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Abstract: In this work we consider isolation from side in different degree structures, in particular, in the $2$-computably enumerable $wtt$-degrees and in low Turing degrees. Intuitively, a $2$-computably enumerable degree is isolated from side if all computably enumerable degrees from its lower cone are bounded from above by some computably enumerable degree which is incomparable with the given one. It is proved that any properly $2$-computably enumerable $wtt$-degree is isolated from side by some computable enumerable $wtt$-degree. Also it is shown that the same result holds for the low $2$-computable enumerable Turing degrees.
Keywords: $2$-computably enumerable set, $wtt$-degree, Turing degree, isolation from side.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-00420_мол_а
Received: 26.03.2020
Revised: 26.03.2020
Accepted: 29.06.2020
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2020, Volume 64, Issue 8, Pages 70–73
DOI: https://doi.org/10.3103/S1066369X20080095
Bibliographic databases:
Document Type: Article
UDC: 510.535
Language: Russian
Citation: M. M. Yamaleev, “Isolation from side in $2$-computably enumerable degrees”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 8, 81–86; Russian Math. (Iz. VUZ), 64:8 (2020), 70–73
Citation in format AMSBIB
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\paper Isolation from side in $2$-computably enumerable degrees
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\issue 8
\pages 70--73
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  • This publication is cited in the following 2 articles:
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    Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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