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Algebra Logika, 2008, Volume 47, Number 1, Pages 94–107 (Mi al348)  

This article is cited in 14 scientific papers (total in 14 papers)

A weak form of interpolation in equational logic

L. L. Maksimova

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

Abstract: The notions of a weak interpolation property and of weak amalgamation are introduced. It is proved that in varieties with the congruence extension property, the weak interpolation property is equivalent to the weak amalgamation property. In turn, weak amalgamability of a variety is equivalent to amalgamability of a class of finitely generated simple algebras in this variety.

Keywords: weak interpolation property, weak amalgamation, variety with congruence extension property.

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English version:
Algebra and Logic, 2008, 47:1, 56–64

Bibliographic databases:

UDC: 510.64
Received: 06.03.2007

Citation: L. L. Maksimova, “A weak form of interpolation in equational logic”, Algebra Logika, 47:1 (2008), 94–107; Algebra and Logic, 47:1 (2008), 56–64

Citation in format AMSBIB
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\paper A weak form of interpolation in equational logic
\jour Algebra Logika
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\vol 47
\issue 1
\pages 94--107
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\yr 2008
\vol 47
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\pages 56--64
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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, E. Orlowska, “The Beth property and interpolation in lattice-based algebras and logics”, Algebra and Logic, 47:3 (2008), 176–192  mathnet  crossref  mathscinet  zmath
    2. A. V. Karpenko, “Weak interpolation in extensions of the logics $S4$ and $K4$”, Algebra and Logic, 47:6 (2008), 395–404  mathnet  crossref  mathscinet  zmath  isi
    3. 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
    4. A. V. Karpenko, “Interpolation properties in the extensions of the logic of inequality”, Siberian Math. J., 51:3 (2010), 439–451  mathnet  crossref  mathscinet  zmath  isi
    5. L. L. Maksimova, “Joint consistency in extensions of the minimal logic”, Siberian Math. J., 51:3 (2010), 479–490  mathnet  crossref  mathscinet  zmath  isi
    6. A. V. Karpenko, L. L. Maksimova, “Simple weakly transitive modal algebras”, Algebra and Logic, 49:3 (2010), 233–245  mathnet  crossref  mathscinet  zmath
    7. 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
    8. 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
    9. Maksimova L., “Interpolation and Definability Over the Logic Gl”, Stud. Log., 99:1-3, SI (2011), 249–267  crossref  mathscinet  zmath  isi  elib  scopus
    10. 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
    11. 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
    12. L. L. Maksimova, “The projective Beth property in well-composed logics”, Algebra and Logic, 52:2 (2013), 116–136  mathnet  crossref  mathscinet  isi
    13. L. L. Maksimova, “Restricted interpolation over modal logic $\mathrm S4$”, Algebra and Logic, 52:4 (2013), 308–335  mathnet  crossref  mathscinet  isi
    14. Karpenko A., “Decidability of Some Interpolation Properties For Weakly Transitive Modal Logics”, Larisa Maksimova on Implication, Interpolation, and Definability, Outstanding Contributions to Logic, 15, ed. Odintsov S., Springer, 2018, 171–183  crossref  mathscinet  isi
  • Алгебра и логика Algebra and Logic
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