|
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
 Full text:
PDF file (251 kB)
References:
PDF file
HTML file
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}
Linking options:
http://mi.mathnet.ru/eng/al64 http://mi.mathnet.ru/eng/al/v44/i1/p3
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:
-
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
 -
M. N. Leontyeva, “Sufficient Conditions of Decidability of Boolean Algebras”, J. Math. Sci., 195:6 (2013), 827–831
-
M. N. Leontyeva, “The minimality of certain decidability conditions for Boolean algebras”, Siberian Math. J., 53:1 (2012), 106–118
 -
Leontyeva M.N., “The Existence of Strongly Computable Representations in the Class of Boolean Algebras”, Dokl. Math., 86:1 (2012), 469–471
 -
M. N. Leontieva, “Strong constructivizability of Boolean algebras of elementary characteristic $(\infty,0,0)$”, Algebra and Logic, 53:2 (2014), 119–132
|
| Number of views: |
| This page: | 321 | | Full text: | 104 | | References: | 34 | | First page: | 1 |
|
Terms of Use