Geodesic
Infinitely many functional pre-complete classes of formulas in the propositional provability intuitionistic logic
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2007), pp. 66-72 
A. Rusu. Infinitely many functional pre-complete classes of formulas in the propositional provability intuitionistic logic. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2007), pp. 66-72. http://geodesic.mathdoc.fr/item/BASM_2007_1_a5/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the propositional provability intuitionistic logic $I^\Delta$, introduced by A. V. Kuznetsov [2]. We prove that there are infinitely many classes of formulas in the calculus of $I^\Delta$, which are pre-complete with respect to functional expressibility in $I^\Delta$. This result is stronger than an ealier one stated by the author in [1].

[1] Rusu A., “The construction of a numerable collection of pre-complete classes of formulas in an extension of the provability intuitionistic logic”, Youth and Modern Science, Theses of referats of the Second republican conference of young researchers (December, 14–15, 1989), Ştiinţa, Chişinău, 1989, 32–33 (in Russian)

[2] Kuznetsov A. V., “Provability-intuitionistic logic”, Modal and Intensional Logics, The theses of the Coordinative Conference, Moscow, 1978, 75–79 (in Russian)

[3] Kuznetsov A. V., “On provability intuitionistic propositional calculus”, DAN SSSR, 283:1 (1985), 27–30 (in Russian) | MR

[4] Wolter F., Zakharyaschev M., “Intuitionistic Modal Logic”, Logic and Foundations of Mathematics, Selected Contributed Papers of 10th Int. Congress of Logic, Methodology and Philosophy of Science (Florence, August 1995)

[5] Ratsa M. F., “The non-tabularity of the logic $S4$ with respect to functional completeness”, Algebra and Logics, 21 (1982), 283–320 (in Russian) | MR | Zbl

[6] Ratsa M. F., On expressibility in the propositional calculi, Ştiinţa, Chişinău, 1991 (in Russian) | MR

[7] Kuznetsov A. V., “On problems of identity and functional completeness for algebraic systems”, Proceedings of the 3rd all-union mathematical congress, V. 2 (Moscow, 1956), 145–146 (in Russian)

[8] Kuznetsov A. V., “Analogues of the “Sheffer's Stroke” in constructive mathematics”, DAN SSSR, 160:2 (1965), 274–277 (in Russian) | Zbl

[9] Kuznetsov A. V., “On functional expressibility in superintuitionistic logics”, Mathematical Investigations, 6:4 (1971), 75–122 (in Russian) | MR | Zbl

[10] Jablonskij S. V., “Functional constructions in $k$-valued logic”, Proceedings of the Mathematical Institute V. A. Steklov, 51, 1958, 5–142 (in Russian) | MR

[11] Jablonskij S. V., Introduction in Discrete Mathematics, Moscow, 1986 (in Russian)