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Algebra Logika, 2021 Volume 60, Number 2, Pages 195–209 (Mi al2658)

Some properties of the upper semilattice of computable families of computably enumerable sets

M. Kh. Faizrakhmanov

Kazan (Volga Region) Federal University

Abstract: 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.

UDC: 510.5

Received: 11.10.2020
Revised: 24.08.2021

DOI: 10.33048/alglog.2021.60.206


 English version:
Algebra and Logic, 2021, 60:2, 128–138

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© Steklov Math. Inst. of RAS, 2024