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Algebra Logika, 2004, Volume 43, Number 2, Pages 133–158 (Mi al60)  

This article is cited in 9 scientific papers (total in 9 papers)

Computable Homogeneous Boolean Algebras and a Metatheorem

P. E. Alaev

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We consider computable homogeneous Boolean algebras. Previously, countable homogeneous Boolean algebras have been described up to isomorphism and a simple criterion has been found for the existence of a strongly constructive (decidable) isomorphic copy for such. We propose a natural criterion for the existence of a constructive (computable) isomorphic copy. For this, a new hierarchy of $\varnothing^{(\omega)}$ – computable functions and sets is introduced, which is more delicate than Feiner's. Also, a metatheorem is proved connecting computable Boolean algebras and their hyperarithmetical quotient algebras.

Keywords: computable homogeneous Boolean algebra, constructive copy for an algebra, hierarchy

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English version:
Algebra and Logic, 2004, 43:2, 73–87

Bibliographic databases:

UDC: 512.563+510.5+510.6
Received: 23.04.2002

Citation: P. E. Alaev, “Computable Homogeneous Boolean Algebras and a Metatheorem”, Algebra Logika, 43:2 (2004), 133–158; Algebra and Logic, 43:2 (2004), 73–87

Citation in format AMSBIB
\Bibitem{Ala04}
\by P.~E.~Alaev
\paper Computable Homogeneous Boolean Algebras and a Metatheorem
\jour Algebra Logika
\yr 2004
\vol 43
\issue 2
\pages 133--158
\mathnet{http://mi.mathnet.ru/al60}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2072567}
\zmath{https://zbmath.org/?q=an:1062.03034}
\transl
\jour Algebra and Logic
\yr 2004
\vol 43
\issue 2
\pages 73--87
\crossref{https://doi.org/10.1023/B:ALLO.0000020844.03135.a6}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42349103214}


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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. P. E. Alaev, “Computable families of superatomic Boolean algebras”, Siberian Math. J., 44:4 (2003), 561–567  mathnet  crossref  mathscinet  zmath  isi
    2. P. E. Alaev, “Hyperarithmetical Boolean algebras with a distinguished ideal”, Siberian Math. J., 45:5 (2004), 795–805  mathnet  crossref  mathscinet  zmath  isi
    3. P. E. Alaev, “A generalized Feiner hierarchy”, Siberian Math. J., 49:2 (2008), 191–201  mathnet  crossref  mathscinet  zmath  isi
    4. M. N. Leontieva, “Boolean algebras of elementary characteristic (1,0,1) whose set of atoms and Ershov–Tarski ideal are computable”, Algebra and Logic, 50:2 (2011), 93–105  mathnet  crossref  mathscinet  zmath  isi
    5. M. N. Leontyeva, “The minimality of certain decidability conditions for Boolean algebras”, Siberian Math. J., 53:1 (2012), 106–118  mathnet  crossref  mathscinet  isi
    6. Harris K., Montalban A., “On the n-back-and-forth types of boolean algebras”, Trans Amer Math Soc, 364:2 (2012), 827–866  crossref  mathscinet  zmath  isi  scopus
    7. Montalban A., “Counting the Back-and-Forth Types”, J. Logic Comput., 22:4, SI (2012), 857–876  crossref  mathscinet  zmath  isi  scopus
    8. Harris K., Montalban A., “Boolean Algebra Approximations”, Trans. Am. Math. Soc., 366:10 (2014), PII S0002-9947(2014)05950-3, 5223–5256  crossref  mathscinet  zmath  isi  scopus
    9. Bazhenov N., Fokina E., San Mauro L., “Learning Families of Algebraic Structures From Informant”, Inf. Comput., 275 (2020), 104590  crossref  mathscinet  zmath  isi  scopus
  • Алгебра и логика Algebra and Logic
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