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Mat. Tr., 2004, Volume 7, Number 1, Pages 3–12 (Mi mt68)  

This article is cited in 6 scientific papers (total in 6 papers)

Decidable Boolean Algebras of Characteristic $(1,0,1)$

P. E. Alaev

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

Abstract: We prove that every 2-constructive Boolean algebra with elementary characteristic $(1,0,1)$ is strongly constructivizable (decidable). This completes the study of the relation between $n$-constructibility and strong constructibility for Boolean algebras of characteristics $(0,*,*)$ and $(1,*,*)$. In addition, we give a description for 3-constructive Boolean algebras by means of a $\Delta^0_2$-computable invariant.

Key words: Boolean algebra, algorithm, computability, constructive structure.

Full text: PDF file (943 kB)
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English version:
Siberian Advances in Mathematics, 2005, 15:1, 1–10

Bibliographic databases:

UDC: 512.563+510.5+510.6
Received: 24.07.2003

Citation: P. E. Alaev, “Decidable Boolean Algebras of Characteristic $(1,0,1)$”, Mat. Tr., 7:1 (2004), 3–12; Siberian Adv. Math., 15:1 (2005), 1–10

Citation in format AMSBIB
\Bibitem{Ala04}
\by P.~E.~Alaev
\paper Decidable Boolean Algebras of Characteristic~$(1,0,1)$
\jour Mat. Tr.
\yr 2004
\vol 7
\issue 1
\pages 3--12
\mathnet{http://mi.mathnet.ru/mt68}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2068274}
\zmath{https://zbmath.org/?q=an:1074.03509|1062.03035}
\transl
\jour Siberian Adv. Math.
\yr 2005
\vol 15
\issue 1
\pages 1--10


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. P. E. Alaev, “Strongly constructive Boolean algebras”, Algebra and Logic, 44:1 (2005), 1–12  mathnet  crossref  mathscinet  zmath
    2. 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
    3. M. N. Leontyeva, “Sufficient Conditions of Decidability of Boolean Algebras”, J. Math. Sci., 195:6 (2013), 827–831  mathnet  crossref
    4. M. N. Leontyeva, “The minimality of certain decidability conditions for Boolean algebras”, Siberian Math. J., 53:1 (2012), 106–118  mathnet  crossref  mathscinet  isi
    5. 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
    6. 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
  • Математические труды Siberian Advances in Mathematics
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