Geodesic
Some properties of the upper semilattice of computable families of computably enumerable sets
Algebra i logika, Tome 60 (2021) no. 2, pp. 195-209

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We look at specific features of the algebraic structure of an upper semilattice of computable families of computably enumerable sets in $\Omega$. It is proved that ideals of minuend and finite families of $\Omega$ coincide. We deal with the question whether there exist atoms and coatoms in the factor semilattice of $\Omega$ with respect to an ideal of finite families. Also we point out a sufficient condition for computable families to be complemented.
Keywords: computably enumerable set, computable family, computable numbering, semilattice of computable families. 
@article{AL_2021_60_2_a5,
     author = {M. Kh. Faizrakhmanov},
     title = {Some properties of the upper semilattice of computable families of computably enumerable sets},
     journal = {Algebra i logika},
     pages = {195--209},
     publisher = {mathdoc},
     volume = {60},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2021_60_2_a5/}
}
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M. Kh. Faizrakhmanov. Some properties of the upper semilattice of computable families of computably enumerable sets. Algebra i logika, Tome 60 (2021) no. 2, pp. 195-209. http://geodesic.mathdoc.fr/item/AL_2021_60_2_a5/