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Algebra Logika, 2003, Volume 42, Number 1, Pages 65–93 (Mi al18)  

This article is cited in 21 scientific papers (total in 21 papers)

Implicit Definability and Positive Logics

L. L. Maksimova

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

Abstract: We furnish a description of all positive logics possessing the projective Beth property PBP. Decidability of PBP is proved for the positive calculi extending a positive fragment $Int^+$ of the intuitionistic propositional calculus. The results mentioned are applied to explore extensions of Johansson's minimal logic.

Keywords: positive logic, projective Beth property, intuitionistic propositional calculus, Johansson's minimal logic.

Full text: PDF file (272 kB)
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English version:
Algebra and Logic, 2003, 42:1, 37–53

Bibliographic databases:

UDC: 510.64
Received: 07.02.2001

Citation: L. L. Maksimova, “Implicit Definability and Positive Logics”, Algebra Logika, 42:1 (2003), 65–93; Algebra and Logic, 42:1 (2003), 37–53

Citation in format AMSBIB
\Bibitem{Mak03}
\by L.~L.~Maksimova
\paper Implicit Definability and Positive Logics
\jour Algebra Logika
\yr 2003
\vol 42
\issue 1
\pages 65--93
\mathnet{http://mi.mathnet.ru/al18}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1988024}
\zmath{https://zbmath.org/?q=an:1034.03008}
\transl
\jour Algebra and Logic
\yr 2003
\vol 42
\issue 1
\pages 37--53
\crossref{https://doi.org/10.1023/A:1022628824337}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-42249100524}


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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, “Interpolation and Definability in Extensions of the Minimal Logic”, Algebra and Logic, 44:6 (2005), 407–421  mathnet  crossref  mathscinet  zmath
    2. L. L. Maksimova, “The Projective Beth Property and Interpolation in Positive and Related Logics”, Algebra and Logic, 45:1 (2006), 49–66  mathnet  crossref  mathscinet  zmath
    3. L. L. Maksimova, P. A. Shrainer, “Algoritmy raspoznavaniya tablichnosti i predtablichnosti v rasshireniyakh intuitsionistskogo ischisleniya”, Vestn. NGU. Ser. matem., mekh., inform., 6:3 (2006), 49–58  mathnet
    4. L. L. Maksimova, “A method of proving interpolation in paraconsistent extensions of the minimal logic”, Algebra and Logic, 46:5 (2007), 341–353  mathnet  crossref  mathscinet  zmath  isi
    5. L. L. Maksimova, “Restricted interpolation property in superintuitionistic logics”, Algebra and Logic, 48:1 (2009), 33–53  mathnet  crossref  mathscinet  zmath  isi
    6. L. L. Maksimova, “Decidability of the interpolation problem and of related properties in tabular logics”, Algebra and Logic, 48:6 (2009), 426–448  mathnet  crossref  mathscinet  zmath  isi
    7. L. L. Maksimova, “Joint consistency in extensions of the minimal logic”, Siberian Math. J., 51:3 (2010), 479–490  mathnet  crossref  mathscinet  zmath  isi
    8. Maksimova L., “Problem of restricted interpolation in superintuitionistic and some modal logics”, Logic Journal of the Igpl, 18:3 (2010), 367–380  crossref  mathscinet  zmath  isi  elib  scopus
    9. 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
    10. 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
    11. Maksimova L., “Interpolation and Definability Over the Logic Gl”, Stud. Log., 99:1-3, SI (2011), 249–267  crossref  mathscinet  zmath  isi  elib  scopus
    12. 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
    13. 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
    14. Galatos N., Raftery J.G., “A Category Equivalence for Odd Sugihara Monoids and its Applications”, J. Pure Appl. Algebr., 216:10 (2012), 2177–2192  crossref  mathscinet  zmath  isi  scopus
    15. L. L. Maksimova, “The projective Beth property in well-composed logics”, Algebra and Logic, 52:2 (2013), 116–136  mathnet  crossref  mathscinet  isi
    16. L. L. Maksimova, “Negativnaya ekvivalentnost nad minimalnoi logikoi i interpolyatsiya”, Sib. elektron. matem. izv., 11 (2014), 1–17  mathnet
    17. 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
    18. L. L. Maksimova, V. F. Yun, “Ischisleniya nad minimalnoi logikoi i nevlozhimost algebr”, Sib. elektron. matem. izv., 13 (2016), 704–715  mathnet  crossref
    19. Bezhanishvili G., Moraschini T., Raftery J.G., “Epimorphisms in Varieties of Residuated Structures”, J. Algebra, 492 (2017), 185–211  crossref  mathscinet  zmath  isi  scopus
    20. 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
    21. L. L. Maksimova, V. F. Yun, “Uznavaemost v predgeitingovykh i stroinykh logikakh”, Sib. elektron. matem. izv., 16 (2019), 427–434  mathnet  crossref
  • Алгебра и логика Algebra and Logic
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