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Sibirsk. Mat. Zh., 2005, Volume 46, Number 4, Pages 928–941 (Mi smj1015)  

This article is cited in 2 scientific papers (total in 2 papers)

The degree spectra of definable relations on Boolean algebras

P. M. Semukhin

Novosibirsk State University, Mechanics and Mathematics Department

Abstract: We study some questions concerning the structure of the spectra of the sets of atoms and atomless elements in a computable Boolean algebra. We prove that if the spectrum of the set of atoms contains a 1-low degree then it contains a computable degree. We show also that in a computable Boolean algebra of characteristic $(1,1,0)$ whose set of atoms is computable the spectrum of the atomless ideal consists of all $\Pi_2^0$ degrees.

Keywords: Boolean algebras, computable models, spectra of relations

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English version:
Siberian Mathematical Journal, 2005, 46:4, 740–750

Bibliographic databases:

UDC: 510.5, 512.563
Received: 16.07.2003
Revised: 27.04.2005

Citation: P. M. Semukhin, “The degree spectra of definable relations on Boolean algebras”, Sibirsk. Mat. Zh., 46:4 (2005), 928–941; Siberian Math. J., 46:4 (2005), 740–750

Citation in format AMSBIB
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\by P.~M.~Semukhin
\paper The degree spectra of definable relations on Boolean algebras
\jour Sibirsk. Mat. Zh.
\yr 2005
\vol 46
\issue 4
\pages 928--941
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2169408}
\zmath{https://zbmath.org/?q=an:1119.03042}
\transl
\jour Siberian Math. J.
\yr 2005
\vol 46
\issue 4
\pages 740--750
\crossref{https://doi.org/10.1007/s11202-005-0074-2}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000231331700017}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. A. Bazhenov, “Degrees of categoricity for superatomic Boolean algebras”, Algebra and Logic, 52:3 (2013), 179–187  mathnet  crossref  mathscinet  isi
    2. N. A. Bazhenov, “Boolean algebras with distinguished endomorphisms and generating trees”, J. Math. Sci., 215:4 (2016), 460–474  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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