Geodesic
HKSS-completeness of modal algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 923-930

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The paper studies computability-theoretic properties of countable modal algebras. We prove that the class of modal algebras is complete in the sense of the work of Hirschfeldt, Khoussainov, Shore, and Slinko. This answers an open question of Bazhenov [Stud. Log., 104 (2016), 1083–1097]. The result implies that every degree spectrum and every categoricity spectrum can be realized by a suitable modal algebra.
Keywords: computable structure, Boolean algebra with operators, degree spectrum, categoricity spectrum, first-order definability.
Mots-clés : modal algebra, computable dimension 
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     author = {N. Bazhenov},
     title = {HKSS-completeness of modal algebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {923--930},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a5/}
}
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N. Bazhenov. HKSS-completeness of modal algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 2, pp. 923-930. http://geodesic.mathdoc.fr/item/SEMR_2021_18_2_a5/