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Mat. Sb. (N.S.), 1986, Volume 131(173), Number 3(11), Pages 403–412 (Mi msb1932)  

This article is cited in 1 scientific paper (total in 1 paper)

Algebraic proof of the separation property for an intuitionistic provability calculus

A. U. Muravitskii


Abstract: For intuitionistic provability calculus $I^\Delta$ obtained from the intuitionistic propositional calculus by adjoining to the postulates of the latter the axioms $(p\supset\Delta p)$, $((\Delta p\supset p)\supset p)$ and $(\Delta p\supset(((q\supset p)\supset q)\supset q))$, an algebraic proof is given of the separation property: $I^\Delta\vdash a$ if and only if there exists a derivation of formula $a$ whose terms contain only those connectives that occur in $a$. The proof is achieved by constructing an (isomorphic) embedding of pseudo-Boolean algebras, and on this basis then constructing embeddings, into $\Delta$-pseudo-Boolean algebras, of algebras whose classes approximate corresponding fragments of the calculus $I^\Delta$.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Sbornik, 1988, 59:2, 397–406

Bibliographic databases:

UDC: 510.6
MSC: Primary 03B45; Secondary 03F55, 03G25
Received: 02.06.1985

Citation: A. U. Muravitskii, “Algebraic proof of the separation property for an intuitionistic provability calculus”, Mat. Sb. (N.S.), 131(173):3(11) (1986), 403–412; Math. USSR-Sb., 59:2 (1988), 397–406

Citation in format AMSBIB
\Bibitem{Mur86}
\by A.~U.~Muravitskii
\paper Algebraic proof of the separation property for an intuitionistic provability calculus
\jour Mat. Sb. (N.S.)
\yr 1986
\vol 131(173)
\issue 3(11)
\pages 403--412
\mathnet{http://mi.mathnet.ru/msb1932}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=881921}
\zmath{https://zbmath.org/?q=an:0632.03017|0621.03010}
\transl
\jour Math. USSR-Sb.
\yr 1988
\vol 59
\issue 2
\pages 397--406
\crossref{https://doi.org/10.1070/SM1988v059n02ABEH003142}


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    This publication is cited in the following articles:
    1. J. L. Castiglioni, H. J. San Martín, “On products of posets and coproducts of KM-algebras”, Soft Comput, 2015  crossref  mathscinet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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