Boolean Algebras with Distinguished Endomorphisms and Generating Trees


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We characterize computable Boolean algebras with distinguished endomorphisms in terms of generating trees and mappings of these trees. We show that every degree spectrum of a countable family of subsets of ω is the degree spectrum of some natural enrichment of a Boolean algebra. Bibliography: 20 titles.

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N. Bazhenov

Sobolev Institute of Mathematics SB RAS; Novosibirsk State University

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Email: nickbazh@yandex.ru
俄罗斯联邦, 4, pr. Akad, Novosibirsk, Koptyuga, 630090; 2, ul. Pirogova, Novosibirsk, 630090

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