Bases of admissible rules of the modal system Grz and of intuitionistic logic

It is proved that the free pseudoboolean algebra $F_\omega(\mathrm{Int})$ and the free topoboolean algebra $F_\omega(\mathrm{Grz})$ do not have bases of quasi-identities in a finite number of variables. A corollary is that the intuitionistic propositional logic $\mathrm{Int}$ and the modal system $\mathrm{Grz}$ do not have finite bases of admissible rules. Infinite recursive bases of quasi-identities are found for $F_\omega(\mathrm{Int})$ and $F_\omega(\mathrm{Grz})$. This implies that the problem of admissibility of rules in the logics $\mathrm{Grz}$ and $\mathrm{Int}$ is algorithmically decidable.
Bibligraphy: 14 titles.