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 Algebra Logika: Year: Volume: Issue: Page: Find

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

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

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
\Bibitem{Mak08} \by L.~L.~Maksimova \paper A weak form of interpolation in equational logic \jour Algebra Logika \yr 2008 \vol 47 \issue 1 \pages 94--107 \mathnet{http://mi.mathnet.ru/al348} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2408573} \zmath{https://zbmath.org/?q=an:1164.03319} \transl \jour Algebra and Logic \yr 2008 \vol 47 \issue 1 \pages 56--64 \crossref{https://doi.org/10.1007/s10469-008-0006-x} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000255038400006} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-40549113650} 

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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
2. A. V. Karpenko, “Weak interpolation in extensions of the logics $S4$ and $K4$”, Algebra and Logic, 47:6 (2008), 395–404
3. L. L. Maksimova, “Decidability of the interpolation problem and of related properties in tabular logics”, Algebra and Logic, 48:6 (2009), 426–448
4. A. V. Karpenko, “Interpolation properties in the extensions of the logic of inequality”, Siberian Math. J., 51:3 (2010), 439–451
5. L. L. Maksimova, “Joint consistency in extensions of the minimal logic”, Siberian Math. J., 51:3 (2010), 479–490
6. A. V. Karpenko, L. L. Maksimova, “Simple weakly transitive modal algebras”, Algebra and Logic, 49:3 (2010), 233–245
7. L. L. Maksimova, “Decidability of the weak interpolation property over the minimal logic”, Algebra and Logic, 50:2 (2011), 106–132
8. L. L. Maksimova, “Amalgamation, Interpolation and Implicit Definability in Varieties of Algebras”, Proc. Steklov Inst. Math., 278, suppl. 1 (2012), S66–S90
9. Maksimova L., “Interpolation and Definability Over the Logic Gl”, Stud. Log., 99:1-3, SI (2011), 249–267
10. L. L. Maksimova, “Interpolation and the projective Beth property in well-composed logics”, Algebra and Logic, 51:2 (2012), 163–184
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
12. L. L. Maksimova, “The projective Beth property in well-composed logics”, Algebra and Logic, 52:2 (2013), 116–136
13. L. L. Maksimova, “Restricted interpolation over modal logic $\mathrm S4$”, Algebra and Logic, 52:4 (2013), 308–335
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
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