This article is cited 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

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.

UDC: 510.535

Received: 26.03.2020
Revised: 26.03.2020
Accepted: 29.06.2020

DOI: 10.26907/0021-3446-2020-8-81-86

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:8, 70–73

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