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Algebra Logika, 2005, Volume 44, Number 1, Pages 3–23 (Mi al64)  

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

Strongly constructive Boolean algebras

P. E. Alaev

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

Abstract: A computable structure is said to be $n$-constructive if there exists an algorithm which, given a finite $\Sigma_n$-formula and a tuple of elements, determines whether that tuple satisfies this formula. A structure is strongly constructive if such an algorithm exists for all formulas of the predicate calculus, and is decidable if it has a strongly constructive isomorphic copy. We give a complete description of relations between $n$-constructibility and decidability for Boolean algebras of a fixed elementary characteristic.

Keywords: computable structure, Boolean algebra, $n$-constructive structure, strongly constructive structure, decidable structure

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English version:
Algebra and Logic, 2005, 44:1, 1–12

Bibliographic databases:

UDC: 512.563+510.5+510.6
Received: 16.01.2004

Citation: P. E. Alaev, “Strongly constructive Boolean algebras”, Algebra Logika, 44:1 (2005), 3–23; Algebra and Logic, 44:1 (2005), 1–12

Citation in format AMSBIB
\Bibitem{Ala05}
\by P.~E.~Alaev
\paper Strongly constructive Boolean algebras
\jour Algebra Logika
\yr 2005
\vol 44
\issue 1
\pages 3--23
\mathnet{http://mi.mathnet.ru/al64}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2165870}
\zmath{https://zbmath.org/?q=an:1096.03043}
\transl
\jour Algebra and Logic
\yr 2005
\vol 44
\issue 1
\pages 1--12
\crossref{https://doi.org/10.1007/s10469-005-0001-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-17444383499}


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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. M. N. Leontyeva, “Boolean Algebras of Elementary Characteristic $(1,0,1)$ with the Computable Set of Atoms and the Ideal of Atomic Elements”, J. Math. Sci., 186:3 (2012), 461–465  mathnet  crossref
    2. M. N. Leontyeva, “Sufficient Conditions of Decidability of Boolean Algebras”, J. Math. Sci., 195:6 (2013), 827–831  mathnet  crossref
    3. M. N. Leontyeva, “The minimality of certain decidability conditions for Boolean algebras”, Siberian Math. J., 53:1 (2012), 106–118  mathnet  crossref  mathscinet  isi
    4. Leontyeva M.N., “The Existence of Strongly Computable Representations in the Class of Boolean Algebras”, Dokl. Math., 86:1 (2012), 469–471  crossref  mathscinet  zmath  isi  elib  elib  scopus
    5. M. N. Leontieva, “Strong constructivizability of Boolean algebras of elementary characteristic $(\infty,0,0)$”, Algebra and Logic, 53:2 (2014), 119–132  mathnet  crossref  mathscinet  isi
  • Алгебра и логика Algebra and Logic
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