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Algebra Logika, 2012, Volume 51, Number 5, Pages 579–607 (Mi al552)  

This article is cited in 5 scientific papers (total in 5 papers)

Constructivizability of the Boolean algebra $\mathfrak B(\omega)$ with a distinguished automorphism

N. A. Bazhenova, R. R. Tukhbatullinab

a Novosibirsk State University, Novosibirsk, Russia
b CERGE–EI, A joint workplace of Charles Univ. and Economics Inst. Acad. Sci. Czech Repub., Prague, Czech Republic

Abstract: A constructivizability criterion for the Boolean algebra $\mathfrak B(\omega)$ with a distinguished ideal is given. As a consequence of the criterion, combined with a result due to I. Kalimullin, B. Khoussainov, and A. Melnikov, we construct a Boolean algebra with a distinguished ideal whose degree spectrum contains every nonzero Turing $\Delta^0_2$-degree but does not contain $0$.

Keywords: Boolean algebra with distinguished automorphism, constructivizability, degree spectra of structures.

Full text: PDF file (309 kB)
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English version:
Algebra and Logic, 2012, 51:5, 384–403

Bibliographic databases:

Document Type: Article
UDC: 512.563+510.5+510.6
Received: 01.11.2011
Revised: 08.08.2012

Citation: N. A. Bazhenov, R. R. Tukhbatullina, “Constructivizability of the Boolean algebra $\mathfrak B(\omega)$ with a distinguished automorphism”, Algebra Logika, 51:5 (2012), 579–607; Algebra and Logic, 51:5 (2012), 384–403

Citation in format AMSBIB
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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, R. R. Tukhbatullina, “Computable categoricity of the Boolean algebra $\mathfrak B(\omega)$ with a distinguished automorphism”, Algebra and Logic, 52:2 (2013), 89–97  mathnet  crossref  mathscinet  isi
    2. N. A. Bazhenov, “Computable numberings of the class of Boolean algebras with distinguished endomorphisms”, Algebra and Logic, 52:5 (2013), 355–366  mathnet  crossref  mathscinet  isi
    3. N. A. Bazhenov, “O 2-vychislimo perechislimykh stepenyakh kategorichnosti bulevykh algebr s vydelennym avtomorfizmom”, Vestn. NGU. Ser. matem., mekh., inform., 14:1 (2014), 19–27  mathnet; N. A. Bazhenov, “D.c.e. degrees of categoricity for Boolean algebras with a distinguished automorphism”, J. Math. Sci., 211:6 (2015), 738–746  crossref
    4. N. A. Bazhenov, “Bulevy algebry s vydelennymi endomorfizmami i porozhdayuschie derevya”, Vestn. NGU. Ser. matem., mekh., inform., 15:1 (2015), 29–44  mathnet; N. A. Bazhenov, “Boolean algebras with distinguished endomorphisms and generating trees”, J. Math. Sci., 215:4 (2016), 460–474  crossref
    5. Bazhenov N., “Categoricity Spectra For Polymodal Algebras”, Stud. Log., 104:6 (2016), 1083–1097  crossref  isi
  • Алгебра и логика Algebra and Logic
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