Geodesic
Boolean algebras realized by c.e. equivalence relations
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 848-855

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Let $E$ be a computably enumerable (c.e.) equivalence relation on the set of natural numbers $\omega$. We consider countable structures where basic functions are computable and respect $E$. If the corresponding quotient structure is a Boolean algebra $B$, then we say that the c.e. relation $E$ realizes $B$. In this paper we study connections between algorithmic properties of $E$ and algebraic properties of Boolean algebras realized by $E$. Also we compare these connections with the corresponding results for linear orders and groups realized by c.e. equivalence relations.
Keywords: computability theory, Boolean algebras, computably enumerable structures.
Mots-clés : equivalence relations 
@article{SEMR_2017_14_a23,
     author = {N. Bazhenov and M. Mustafa and F. Stephan and M. Yamaleev},
     title = {Boolean algebras realized by c.e. equivalence relations},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {848--855},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a23/}
}
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N. Bazhenov; M. Mustafa; F. Stephan; M. Yamaleev. Boolean algebras realized by c.e. equivalence relations. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 848-855. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a23/