Geodesic
Isolation from side in $2$-computably enumerable degrees
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2020), pp. 81-86

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IVM_2020_8_a8,
     author = {M. M. Yamaleev},
     title = {Isolation from side in $2$-computably enumerable degrees},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {81--86},
     publisher = {mathdoc},
     number = {8},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2020_8_a8/}
}
TY  - JOUR
AU  - M. M. Yamaleev
TI  - Isolation from side in $2$-computably enumerable degrees
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2020
SP  - 81
EP  - 86
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2020_8_a8/
LA  - ru
ID  - IVM_2020_8_a8
ER  - 
%0 Journal Article
%A M. M. Yamaleev
%T Isolation from side in $2$-computably enumerable degrees
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2020
%P 81-86
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2020_8_a8/
%G ru
%F IVM_2020_8_a8
M. M. Yamaleev. Isolation from side in $2$-computably enumerable degrees. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 8 (2020), pp. 81-86. http://geodesic.mathdoc.fr/item/IVM_2020_8_a8/