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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.
Received: 11.10.2020 Revised: 24.08.2021
Citation:
M. Kh. Faizrakhmanov, “Some properties of the upper semilattice of computable families of computably enumerable sets”, Algebra Logika, 60:2 (2021), 195–209; Algebra and Logic, 60:2 (2021), 128–138
Linking options:
https://www.mathnet.ru/eng/al2658 https://www.mathnet.ru/eng/al/v60/i2/p195
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