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 Sibirsk. Mat. Zh., 2010, Volume 51, Number 3, Pages 604–619 (Mi smj2111)

Joint consistency in extensions of the minimal logic

L. L. Maksimovaab

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

Abstract: Analogs of Robinson's theorem on joint consistency are found which are equivalent to the weak interpolation property (WIP) in extensions of Johansson's minimal logic J. Although all propositional superintuitionistic logics possess this property, there are J-logics without WIP. It is proved that the problem of the validity of WIP in J-logics can be reduced to the same problem over the logic Gl obtained from J by adding the tertium non datur. Some algebraic criteria for validity of WIP over J and Gl are found.

Keywords: minimal logic, interpolation, joint consistency.

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English version:
Siberian Mathematical Journal, 2010, 51:3, 479–490

Bibliographic databases:

UDC: 510.64

Citation: L. L. Maksimova, “Joint consistency in extensions of the minimal logic”, Sibirsk. Mat. Zh., 51:3 (2010), 604–619; Siberian Math. J., 51:3 (2010), 479–490

Citation in format AMSBIB
\Bibitem{Mak10} \by L.~L.~Maksimova \paper Joint consistency in extensions of the minimal logic \jour Sibirsk. Mat. Zh. \yr 2010 \vol 51 \issue 3 \pages 604--619 \mathnet{http://mi.mathnet.ru/smj2111} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2683102} \zmath{https://zbmath.org/?q=an:1208.03031} \transl \jour Siberian Math. J. \yr 2010 \vol 51 \issue 3 \pages 479--490 \crossref{https://doi.org/10.1007/s11202-010-0050-3} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000279087500012} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77953992804} 

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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, “Decidability of the weak interpolation property over the minimal logic”, Algebra and Logic, 50:2 (2011), 106–132
2. Maksimova L., “Interpolation and Definability Over the Logic Gl”, Stud. Log., 99:1-3, SI (2011), 249–267
3. L. L. Maksimova, “Interpolation and the projective Beth property in well-composed logics”, Algebra and Logic, 51:2 (2012), 163–184
4. L. L. Maksimova, “The decidability of craig's interpolation property in well-composed $\mathrm J$-logics”, Siberian Math. J., 53:5 (2012), 839–852
5. L. L. Maksimova, “The projective Beth property in well-composed logics”, Algebra and Logic, 52:2 (2013), 116–136
6. L. L. Maksimova, V. F. Yun, “Extensions of the minimal logic and the interpolation problem”, Siberian Math. J., 59:4 (2018), 681–693
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