BASES OF ADMISSIBLE RULES OF THE MODAL SYSTEM $ \mathrm{Grz}$ AND OF INTUITIONISTIC LOGIC
Vladimir Vladimirovich Rybakov · Mathematics of the USSR-Sbornik · 1987
It is proved that the free pseudoboolean algebra and the free topoboolean algebra do not have bases of quasi-identities in a finite number of variables. A corollary is that the intuitionistic propositional logic and the modal system do not have finite bases of admissible rules. Infinite recursive bases of quasi-identities are found for and . This implies that the problem of admissibility of rules in the logics and is algorithmically decidable.Bibliography: 14 titles.