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Mat. Zametki, 1977, Volume 22, Issue 1, Pages 69–76 (Mi mz8026)  

This article is cited in 3 scientific papers (total in 3 papers)

The intuitionistic propositional calculus with quantifiers

S. K. Sobolev

V. A. Steklov Mathematical Institute, USSR Academy of Sciences

Abstract: Let $L$ be the language of the intuitionistic propositional calculus $J$ completed by the quantifiers $\forall$ and $\exists$, and let calculus $2J$ in language $L$ contain, besides the axioms of $J$, the axioms $\forall x$ $B(x)\supset B(y)$ and $B(y)\supset\exists x$ $B(x)$. A Kripke semantics is constructed for $2J$ and a completeness theorem is proven. A result of D. Gabbay is generalized concerning the undecidability of $C2J^+$-extension of $2J$ by schemes $\exists x$ $(x\equiv B)$ and $\forall x$ $(A\vee B(x))\supset A\vee\forall x$ $B(x)$ specificially: the undecidability is proven of each $T$ theory in language $L$ such that $[2J]\subseteq T\subseteq[C2J^+]$ ($[2J]$ denotes the set of all theorems of calculus $2J$).

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English version:
Mathematical Notes, 1977, 22:1, 528–532

Bibliographic databases:

UDC: 517.11
Received: 02.07.1975

Citation: S. K. Sobolev, “The intuitionistic propositional calculus with quantifiers”, Mat. Zametki, 22:1 (1977), 69–76; Math. Notes, 22:1 (1977), 528–532

Citation in format AMSBIB
\Bibitem{Sob77}
\by S.~K.~Sobolev
\paper The intuitionistic propositional calculus with quantifiers
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 1
\pages 69--76
\mathnet{http://mi.mathnet.ru/mz8026}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=457155}
\zmath{https://zbmath.org/?q=an:0365.02013}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 1
\pages 528--532
\crossref{https://doi.org/10.1007/BF01147694}


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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. A. D. Yashin, “The Smetanich logic $T^{\Phi}$ and two definitions of a new intuitionistic connective”, Math. Notes, 56:1 (1994), 745–750  mathnet  crossref  mathscinet  zmath  isi
    2. A. D. Yashin, “On the completeness of a new intuitionistic connective”, Math. Notes, 60:3 (1996), 313–320  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. A. D. Yashin, “Interpreting Intuitionistic Propositional Logic in Terms of Intuitionistic Protothetics”, Algebra and Logic, 41:1 (2002), 59–64  mathnet  crossref  mathscinet  zmath
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