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Algebra Logika, 2006, Volume 45, Number 1, Pages 85–113 (Mi al119)  

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

The Projective Beth Property and Interpolation in Positive and Related Logics

L. L. Maksimova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We look at the interplay between the projective Beth property in non-classical logics and interpolation. Previously, we proved that in positive logics as well as in superintuitionistic and modal ones, the projective Beth property PB2 follows from Craig's interpolation property and implies the restricted interpolation property IPR. Here, we show that IPR and PB2 are equivalent in positive logics, and also in extensions of the superintuitionistic logic KC and of the modal logic Grz.2.

Keywords: projective Beth property, restricted interpolation property, positive logic, superintuitionistic logic, modal logic

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English version:
Algebra and Logic, 2006, 45:1, 49–66

Bibliographic databases:

UDC: 510.64
Received: 02.06.2005

Citation: L. L. Maksimova, “The Projective Beth Property and Interpolation in Positive and Related Logics”, Algebra Logika, 45:1 (2006), 85–113; Algebra and Logic, 45:1 (2006), 49–66

Citation in format AMSBIB
\Bibitem{Mak06}
\by L.~L.~Maksimova
\paper The Projective Beth Property and Interpolation in Positive and Related Logics
\jour Algebra Logika
\yr 2006
\vol 45
\issue 1
\pages 85--113
\mathnet{http://mi.mathnet.ru/al119}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2259477}
\zmath{https://zbmath.org/?q=an:1119.03026}
\transl
\jour Algebra and Logic
\yr 2006
\vol 45
\issue 1
\pages 49--66
\crossref{https://doi.org/10.1007/s10469-006-0005-8}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-32544460054}


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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, “Restricted interpolation property in superintuitionistic logics”, Algebra and Logic, 48:1 (2009), 33–53  mathnet  crossref  mathscinet  zmath  isi
    2. Maksimova L., “Problem of restricted interpolation in superintuitionistic and some modal logics”, Log. J. Igpl, 18:3 (2010), 367–380  crossref  mathscinet  zmath  isi  scopus
    3. 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
    4. L. L. Maksimova, “Amalgamation, Interpolation and Implicit Definability in Varieties of Algebras”, Proc. Steklov Inst. Math., 278, suppl. 1 (2012), S66–S90  mathnet  crossref  crossref  isi  elib
    5. Maksimova L., “Interpolation and Definability Over the Logic Gl”, Stud. Log., 99:1-3, SI (2011), 249–267  crossref  mathscinet  zmath  isi  elib  scopus
    6. 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
    7. 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
    8. L. L. Maksimova, “The projective Beth property in well-composed logics”, Algebra and Logic, 52:2 (2013), 116–136  mathnet  crossref  mathscinet  isi
  • Алгебра и логика Algebra and Logic
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