Geodesic
Bases of admissible rules of the modal system Grz and of intuitionistic logic
Sbornik. Mathematics, Tome 56 (1987) no. 2, pp. 311-331

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SM_1987_56_2_a2,
     author = {V. V. Rybakov},
     title = {Bases of admissible rules of the modal system {Grz} and of intuitionistic logic},
     journal = {Sbornik. Mathematics},
     pages = {311--331},
     publisher = {mathdoc},
     volume = {56},
     number = {2},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1987_56_2_a2/}
}
TY  - JOUR
AU  - V. V. Rybakov
TI  - Bases of admissible rules of the modal system Grz and of intuitionistic logic
JO  - Sbornik. Mathematics
PY  - 1987
SP  - 311
EP  - 331
VL  - 56
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1987_56_2_a2/
LA  - en
ID  - SM_1987_56_2_a2
ER  - 
%0 Journal Article
%A V. V. Rybakov
%T Bases of admissible rules of the modal system Grz and of intuitionistic logic
%J Sbornik. Mathematics
%D 1987
%P 311-331
%V 56
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1987_56_2_a2/
%G en
%F SM_1987_56_2_a2
V. V. Rybakov. Bases of admissible rules of the modal system Grz and of intuitionistic logic. Sbornik. Mathematics, Tome 56 (1987) no. 2, pp. 311-331. http://geodesic.mathdoc.fr/item/SM_1987_56_2_a2/