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Extensions of the Minimal Logic and the Interpolation Problem

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Abstract

Under study is the interpolation problem over Johansson’s minimal logic J. We give a detailed exposition of the current state of this difficult problem, establish Craig’s interpolation property for several extensions of J, prove the absence of CIP in some families of extensions of J, and survey the results on interpolation over J. Also, the relationship is discussed between the interpolation properties and the recognizability of logics.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

    L. L. Maksimova & V. F. Yun

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  1. L. L. Maksimova
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  2. V. F. Yun
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Correspondence to L. L. Maksimova.

Additional information

Original Russian Text © 2018 Maksimova L.L. and Yun V.F.

Novosibirsk. Translated from Sibirskii Matematicheskii Zhurnal, vol. 59, no. 4, pp. 863–878, July–August, 2018; DOI: 10.17377/smzh.2018.59.410.

The authors were supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh–6848.2016.1).

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Maksimova, L.L., Yun, V.F. Extensions of the Minimal Logic and the Interpolation Problem. Sib Math J 59, 681–693 (2018). https://doi.org/10.1134/S0037446618040109

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  • DOI: https://doi.org/10.1134/S0037446618040109

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