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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2021, Volume 18, Issue 2, Pages 923–930
DOI: https://doi.org/10.33048/semi.2021.18.070 (Mi semr1411) 		 
Mathematical logic, algebra and number theory

HKSS-completeness of modal algebras

N. Bazhenov

Sobolev Institute of Mathematics, 4, Acad. Koptyug ave., Novosibirsk, 630090, Russia
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DOI: https://doi.org/10.33048/semi.2021.18.070
Abstract: 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: modal algebra, computable structure, Boolean algebra with operators, degree spectrum, categoricity spectrum, computable dimension, first-order definability.
Funding agency Grant number
Russian Foundation for Basic Research 20-31-70006
The reported study was funded by RFBR, project number 20-31-70006.
Received April 9, 2021, published September 1, 2021
Bibliographic databases:
Document Type: Article
UDC: 510.5
MSC: 03C57
Language: English
Citation: N. Bazhenov, “HKSS-completeness of modal algebras”, Sib. Èlektron. Mat. Izv., 18:2 (2021), 923–930
Citation in format AMSBIB
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\by N.~Bazhenov
\paper HKSS-completeness of modal algebras
\jour Sib. \`Elektron. Mat. Izv.
\yr 2021
\vol 18
\issue 2
\pages 923--930
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\crossref{https://doi.org/10.33048/semi.2021.18.070}
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