This article is cited in 12 papers

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

V. V. Rybakov


Abstract: 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.

UDC: 510.6+512

MSC: Primary 03B45; Secondary 03F55

Received: 07.06.1984

 English version: Mathematics of the USSR-Sbornik, 1987, 56:2, 311–331

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