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Algebra Logika, 2013, Volume 52, Number 2, Pages 172–202 (Mi al581)  

This article is cited in 5 scientific papers (total in 5 papers)

The projective Beth property in well-composed logics

L. L. Maksimovaab

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

Abstract: The interpolation and Beth definability problems are proved decidable in well-composed logics, i.e., in extensions of Johansson's minimal logic $\mathrm J$ satisfying an axiom $(\perp\to A)\vee(A\to\perp)$. In previous studies, all $\mathrm J$-logics with the weak interpolation property (WIP) were described and WIP was proved decidable over $\mathrm J$. Also it was shown that only finitely many wellcomposed logics possess Craig's interpolation property (CIP) and the restricted interpolation property (IPR), and moreover, IPR is equivalent to the projective Beth property (PBP) on the class of logics in question. These results are applied to prove decidability of IPR and PBP in well-composed logics. The decidability of CIP in such logics was stated earlier. Thus all basic versions of the interpolation and Beth properties are decidable on the class of wellcomposed logics.

Keywords: projective Beth property, interpolation property, decidability, well-composed logic.

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English version:
Algebra and Logic, 2013, 52:2, 116–136

Bibliographic databases:

UDC: 510.64
Received: 21.11.2011

Citation: L. L. Maksimova, “The projective Beth property in well-composed logics”, Algebra Logika, 52:2 (2013), 172–202; Algebra and Logic, 52:2 (2013), 116–136

Citation in format AMSBIB
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\paper The projective Beth property in well-composed logics
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\vol 52
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\pages 172--202
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\pages 116--136
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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, “Negativnaya ekvivalentnost nad minimalnoi logikoi i interpolyatsiya”, Sib. elektron. matem. izv., 11 (2014), 1–17  mathnet
    2. L. L. Maksimova, V. F. Yun, “Interpolation over the minimal logic and Odintsov intervals”, Siberian Math. J., 56:3 (2015), 476–489  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. L. L. Maksimova, V. F. Yun, “Recognizable logics”, Algebra and Logic, 54:2 (2015), 167–182  mathnet  crossref  crossref  mathscinet  isi
    4. L. L. Maksimova, “Recognizable and perceptible logics and varieties”, Algebra and Logic, 56:3 (2017), 245–250  mathnet  crossref  crossref  mathscinet  isi
    5. 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
  • Алгебра и логика Algebra and Logic
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