Interpreting Intuitionistic Propositional Logic in Terms of Intuitionistic Protothetics
Algebra i logika, Tome 41 (2002) no. 1, pp. 104-113.

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

An algebra of sentences of the quite intuitionistic protothetics, that is, an intuitionistic propositional logic with quantifiers augmented by the negation of the excluded middle, is a faithful model of intuitionistic propositional logic.
Keywords: quite intuitionistic protothetics, intuitionistic propositional logic, interpretation, completeness theorem.
@article{AL_2002_41_1_a5,
     author = {A. D. Yashin},
     title = {Interpreting {Intuitionistic} {Propositional} {Logic} in {Terms} of {Intuitionistic} {Protothetics}},
     journal = {Algebra i logika},
     pages = {104--113},
     publisher = {mathdoc},
     volume = {41},
     number = {1},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2002_41_1_a5/}
}
TY  - JOUR
AU  - A. D. Yashin
TI  - Interpreting Intuitionistic Propositional Logic in Terms of Intuitionistic Protothetics
JO  - Algebra i logika
PY  - 2002
SP  - 104
EP  - 113
VL  - 41
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2002_41_1_a5/
LA  - ru
ID  - AL_2002_41_1_a5
ER  - 
%0 Journal Article
%A A. D. Yashin
%T Interpreting Intuitionistic Propositional Logic in Terms of Intuitionistic Protothetics
%J Algebra i logika
%D 2002
%P 104-113
%V 41
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2002_41_1_a5/
%G ru
%F AL_2002_41_1_a5
A. D. Yashin. Interpreting Intuitionistic Propositional Logic in Terms of Intuitionistic Protothetics. Algebra i logika, Tome 41 (2002) no. 1, pp. 104-113. http://geodesic.mathdoc.fr/item/AL_2002_41_1_a5/

[1] C. A. Smorynski, “Applications of Kripke models”, Mathematical investigation of intuitionistic arithmetic and analysis, Lect. Notes Math., 344, ed. A. S. Troelstra, 1973, 324–391 | MR

[2] A. D. Yashin, “Ob interpretatsii intuitsionistskoi logiki vyskazyvanii v intuitsionistskoi prototetike”, Tezisy Mezhd. konf. “Logika i prilozheniya”, Novosibirsk, 2000, 110

[3] S. K. Sobolev, “Ob intuitsionistskom ischislenii vyskazyvanii s kvantorami”, Matem. zametki, 22:1 (1977), 69–76 | MR | Zbl

[4] D. Gabbay, “On 2-nd order intuuitionistic propositional calculus with full comprehension”, Arch. Math. Logik Grundlagenforsch., 16:3–4 (1974), 177–186 | DOI | MR | Zbl

[5] A. G. Dragalin, “Algebraicheskie modeli intuitsionistskikh teorii”, Logicheskii vyvod, Nauka, M., 1979 | MR | Zbl

[6] A. Chërch, Vvedenie v matematicheskuyu logiku, t. 1, IL, M., 1960

[7] D. Pravits, Naturalnyi vyvod, LORI, M., 1997

[8] G. K. Dardzhaniya, “Sekventsialnyi variant modalnoi sistemy $I^\Delta$”, Metalogicheskie issledovaniya, M., 1985, 59–72

[9] A. D. Yashin, “Irreflexive modality in the intuitionistic propositional logic and Novikov completeness”, J. Philos. Log., 28:2 (1999), 175–197 | DOI | MR | Zbl

[10] R. E. Kirk, “A characterization of the classes of finite tree frames which are adequate for the intuitionistic logic”, Z. Math. Logik Grundlagen Math., 26:6 (1980), 497–501 | DOI | MR | Zbl

[11] A. D. Yashin, “Logika Smetanicha $T^\Phi$ i dva opredeleniya novoi intuitsionistskoi svyazki”, Matem. zametki, 56:1 (1994), 135–142 | MR | Zbl