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.
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Original Russian Text Copyright © 2010 Maksimova L. L.
The author was supported by the Russian Foundation for Basic Research (Grant 09-01-00090a), the Leading Scientific Schools of the Russian Federation (Grant NSh-3606.2010.1), and the Russian Federal Agency for Education (Grant 2.1.1.419)
To Yuriĭ Leonidovich Ershov.
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 3, pp. 604–619, May–June, 2010.
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Maksimova, L.L. Joint consistency in extensions of the minimal logic. Sib Math J 51, 479–490 (2010). https://doi.org/10.1007/s11202-010-0050-3
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DOI: https://doi.org/10.1007/s11202-010-0050-3