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Sibirsk. Mat. Zh., 2015, Volume 56, Number 3, Pages 600–616 (Mi smj2663)  

This article is cited in 3 scientific papers (total in 3 papers)

Interpolation over the minimal logic and Odintsov intervals

L. L. Maksimovaa, V. F. Yunab

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

Abstract: We study Craig's interpolation property in the extensions of Johansson's minimal logic. We consider the Odintsov classification of J-logics according to their intuitionistic and negative companions which subdivides all logics into intervals. We prove that the lower endpoint of an interval has Craig interpolation property if and only if both its companions do so. We also establish the recognizability of the lower and upper endpoints which have Craig interpolation property, and find their semantic characterization.

Keywords: Johansson minimal logic, Craig interpolation property, recognizability, Odintsov interval.

DOI: https://doi.org/10.17377/smzh.2015.56.311

Full text: PDF file (337 kB)
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English version:
Siberian Mathematical Journal, 2015, 56:3, 476–489

Bibliographic databases:

UDC: 510.64
Received: 08.09.2014

Citation: L. L. Maksimova, V. F. Yun, “Interpolation over the minimal logic and Odintsov intervals”, Sibirsk. Mat. Zh., 56:3 (2015), 600–616; Siberian Math. J., 56:3 (2015), 476–489

Citation in format AMSBIB
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\jour Sibirsk. Mat. Zh.
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\vol 56
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\pages 600--616
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\jour Siberian Math. J.
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\pages 476--489
\crossref{https://doi.org/10.1134/S0037446615030118}
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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, 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
    2. L. L. Maksimova, V. F. Yun, “The interpolation problem in finite-layered pre-Heyting logics”, Algebra and Logic, 58:2 (2019), 144–157  mathnet  crossref  crossref  isi
    3. L. L. Maksimova, “Constructive classifications of modal logics and extensions of minimal logic”, Algebra and Logic, 58:6 (2020), 540–545  mathnet  crossref  crossref  isi
  • Сибирский математический журнал Siberian Mathematical Journal
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