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Sibirsk. Mat. Zh., 2010, Volume 51, Number 3, Pages 604–619 (Mi smj2111)  

This article is cited in 6 scientific papers (total in 6 papers)

Joint consistency in extensions of the minimal logic

L. L. Maksimovaab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University, Mechanics and Mathematics Department, Novosibirsk

Abstract: Analogs of Robinson's theorem on joint consistency are found which are equivalent to the weak interpolation property (WIP) in extensions of Johansson's minimal logic J. Although all propositional superintuitionistic logics possess this property, there are J-logics without WIP. It is proved that the problem of the validity of WIP in J-logics can be reduced to the same problem over the logic Gl obtained from J by adding the tertium non datur. Some algebraic criteria for validity of WIP over J and Gl are found.

Keywords: minimal logic, interpolation, joint consistency.

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English version:
Siberian Mathematical Journal, 2010, 51:3, 479–490

Bibliographic databases:

UDC: 510.64
Received: 01.02.2010

Citation: L. L. Maksimova, “Joint consistency in extensions of the minimal logic”, Sibirsk. Mat. Zh., 51:3 (2010), 604–619; Siberian Math. J., 51:3 (2010), 479–490

Citation in format AMSBIB
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\by L.~L.~Maksimova
\paper Joint consistency in extensions of the minimal logic
\jour Sibirsk. Mat. Zh.
\yr 2010
\vol 51
\issue 3
\pages 604--619
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\jour Siberian Math. J.
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\issue 3
\pages 479--490
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    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. L. L. Maksimova, “Decidability of the weak interpolation property over the minimal logic”, Algebra and Logic, 50:2 (2011), 106–132  mathnet  crossref  mathscinet  zmath  isi
    2. Maksimova L., “Interpolation and Definability Over the Logic Gl”, Stud. Log., 99:1-3, SI (2011), 249–267  crossref  mathscinet  zmath  isi  elib  scopus
    3. L. L. Maksimova, “Interpolation and the projective Beth property in well-composed logics”, Algebra and Logic, 51:2 (2012), 163–184  mathnet  crossref  mathscinet  zmath  isi
    4. L. L. Maksimova, “The decidability of craig's interpolation property in well-composed $\mathrm J$-logics”, Siberian Math. J., 53:5 (2012), 839–852  mathnet  crossref  mathscinet  isi
    5. L. L. Maksimova, “The projective Beth property in well-composed logics”, Algebra and Logic, 52:2 (2013), 116–136  mathnet  crossref  mathscinet  isi
    6. L. L. Maksimova, V. F. Yun, “Extensions of the minimal logic and the interpolation problem”, Siberian Math. J., 59:4 (2018), 681–693  mathnet  crossref  crossref  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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