Geodesic
On finite approximability of superintuitionistic logics
Sbornik. Mathematics, Tome 31 (1977) no. 2, pp. 257-268 
S. K. Sobolev. On finite approximability of superintuitionistic logics. Sbornik. Mathematics, Tome 31 (1977) no. 2, pp. 257-268. http://geodesic.mathdoc.fr/item/SM_1977_31_2_a8/
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     author = {S. K. Sobolev},
     title = {On finite approximability of superintuitionistic logics},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_31_2_a8/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Finite approximability is proved for superintuitionistic propositional logics generated by formulas satisfying a certain sufficient condition. As a corollary, one obtains the finite approximability of logics generated by formulas with one variable. A formula with two variables is constructed which generates a logic not finitely approximable. All previously known finitely approximable logics have been generated by formulas in three or more variables (see RZhMat., 1971, 5A64 and 1972, 6A84). Figures: 1. Bibliography: 6 titles.

[1] A. V. Kuznetsov, V. Ya. Gerchiu, “O superintuitsionistskikh logikakh i finitnoi approksimiruemosti”, DAN SSSR, 195:5 (1970), 1029–1032 | Zbl

[2] V. Ya. Gerchiu, “O finitnoi approksimiruemosti”, Matem. issledovaniya, 7:1 (1972), 186–192 | MR | Zbl

[3] I. Nishimura, “On formulas of variables”, J. Symb. Log., 25:4 (1960), 327–331 | DOI | MR | Zbl

[4] A. Diego, “Sur les algèbres de Hilbert”, Collect. log. math., Ser. A, 21, Paris, 1966 | MR

[5] C. G. McKay, “Decidability of certain intermediate propositional logics”, J. Symb. Log., 33:2 (1968), 258–264 | DOI | MR | Zbl

[6] K. Fine, “Logic containing $\mathrm{S}4$ without fmp”, Lect. notes in Math., 255 (1972), 98–102 | DOI | MR | Zbl