RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Sb. (N.S.), 1985, Volume 128(170), Number 3(11), Pages 321–338 (Mi msb2162)  

This article is cited in 8 scientific papers (total in 8 papers)

Bases of admissible rules of the modal system Grz and of intuitionistic logic

V. V. Rybakov


Abstract: It is proved that the free pseudoboolean algebra $F_\omega(\mathrm{Int})$ and the free topoboolean algebra $F_\omega(\mathrm{Grz})$ do not have bases of quasi-identities in a finite number of variables. A corollary is that the intuitionistic propositional logic $\mathrm{Int}$ and the modal system $\mathrm{Grz}$ do not have finite bases of admissible rules. Infinite recursive bases of quasi-identities are found for $F_\omega(\mathrm{Int})$ and $F_\omega(\mathrm{Grz})$. This implies that the problem of admissibility of rules in the logics $\mathrm{Grz}$ and $\mathrm{Int}$ is algorithmically decidable.
Bibligraphy: 14 titles.

Full text: PDF file (1207 kB)
References: PDF file   HTML file

English version:
Mathematics of the USSR-Sbornik, 1987, 56:2, 311–331

Bibliographic databases:

UDC: 510.6+512
MSC: Primary 03B45; Secondary 03F55
Received: 07.06.1984

Citation: V. V. Rybakov, “Bases of admissible rules of the modal system Grz and of intuitionistic logic”, Mat. Sb. (N.S.), 128(170):3(11) (1985), 321–338; Math. USSR-Sb., 56:2 (1987), 311–331

Citation in format AMSBIB
\Bibitem{Ryb85}
\by V.~V.~Rybakov
\paper Bases of admissible rules of the modal system Grz and of intuitionistic logic
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 128(170)
\issue 3(11)
\pages 321--338
\mathnet{http://mi.mathnet.ru/msb2162}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=815267}
\zmath{https://zbmath.org/?q=an:0617.03007}
\transl
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 2
\pages 311--331
\crossref{https://doi.org/10.1070/SM1987v056n02ABEH003038}


Linking options:
  • http://mi.mathnet.ru/eng/msb2162
  • http://mi.mathnet.ru/eng/msb/v170/i3/p321

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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:
    1. V. V. Rybakov, “Admissibility of rules of inference, and logical equations, in modal logics axiomatizing provability”, Math. USSR-Izv., 36:2 (1991), 369–390  mathnet  crossref  mathscinet  zmath  adsnasa
    2. V.V. Rybakov, “Problems of substitution and admissibility in the modal system Grz and in intuitionistic propositional calculus”, Annals of Pure and Applied Logic, 50:1 (1990), 71  crossref
    3. Rybakov V., “Admission of the Inherence Rules with Parameters for the Intuitionistic Logics and the Intuitionistic Kripke Models”, 312, no. 1, 1990, 42–45  mathscinet  zmath  isi
    4. Ronald Fagin, J.Y.. Halpern, M.Y.. Vardi, “What is an inference rule?”, J. symb. log, 57:03 (1992), 1018  crossref
    5. Vladimir V. Rybakov, “Intermediate logics preserving admissible inference rules of heyting calculus”, MLQ-Math Log Quart, 39:1 (1993), 403  crossref  mathscinet  zmath
    6. B. R. Fedorishin, “An explicit basis for the admissible inference rules in the Gödel–Löb logic $GL$”, Siberian Math. J., 48:2 (2007), 339–345  mathnet  crossref  mathscinet  zmath  isi  elib
    7. V. V. Rimatskii, “An explicit basis for admissible inference rules in table modal logics of width 2”, Algebra and Logic, 48:1 (2009), 72–86  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    8. V. V. Rimatskii, “Table admissible inference rules”, Algebra and Logic, 48:3 (2009), 228–236  mathnet  crossref  mathscinet  zmath  isi  elib  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
    Number of views:
    This page:209
    Full text:67
    References:19

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020