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 Algebra Logika: Year: Volume: Issue: Page: Find

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

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

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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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
2. M. N. Leontyeva, “Sufficient Conditions of Decidability of Boolean Algebras”, J. Math. Sci., 195:6 (2013), 827–831
3. M. N. Leontyeva, “The minimality of certain decidability conditions for Boolean algebras”, Siberian Math. J., 53:1 (2012), 106–118
4. Leontyeva M.N., “The Existence of Strongly Computable Representations in the Class of Boolean Algebras”, Dokl. Math., 86:1 (2012), 469–471
5. M. N. Leontieva, “Strong constructivizability of Boolean algebras of elementary characteristic $(\infty,0,0)$”, Algebra and Logic, 53:2 (2014), 119–132
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