Separability of normalizable superintuitionistic propositional logics

The problem of separability of superintuitionistic propositional logics that are extensions of the intuitionistic propositional logic is studied. A criterion of separability of normal superintuitionistic propositional logics, as well as results concerning the completeness of their subcalculi is obtained. This criterion makes it possible to determine whether a normalizable superintuitionistic propositional logic is separable. By means of these results, the mistakes discovered by the author in the proofs of certain statements by McKay and Hosoi are corrected.Translated fromMatematicheskie Zametki, Vol. 64, No. 4, pp. 606–615, October, 1998.This research was supported by the Russian Foundation for Basic Research under grant No. 94-01-00944.