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On a fragment of intuitionistic logic which is complete with respect to the Kripke frames with finite domains. (English. Russian original) Zbl 0947.03009
Sib. Math. J. 41, No. 2, 389-396 (2000); translation from Sib. Mat. Zh. 41, No. 2, 470-479 (2000).
The author proves that the fragment of intuitionistic logic without disjunction and existential quantification is complete with respect to the Kripke frames with finite domains. The author also proves this fragment to possess the relaxed interpolation property and the Beth property. It is well known that neither classical nor intuitionistic logic is complete with respect to such Kripke frames.
MSC:
03B20 Subsystems of classical logic (including intuitionistic logic)
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