Geodesic
Classification of Novikov Complete Logics with Extra Logical Constants
Algebra i logika, Tome 42 (2003) no. 3, pp. 366-383.

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We give an exhaustive classification of Novikov complete extensions of the intuitionistic propositional logic in a language with extra logical constants.
Keywords: intuitionistic logic, logical constant, Novikov completeness. 
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A. D. Yashin. Classification of Novikov Complete Logics with Extra Logical Constants. Algebra i logika, Tome 42 (2003) no. 3, pp. 366-383. http://geodesic.mathdoc.fr/item/AL_2003_42_3_a6/

[1] Ya. S. Smetanich, “O polnote ischisleniya vyskazyvanii s dopolnitelnoi operatsiei ot odnoi peremennoi”, Trudy Mosk. matem. ob-va, 9 (1960), 357–371 | Zbl

[2] Ya. S. Smetanich, “Ob ischisleniyakh vyskazyvanii s dopolnitelnoi operatsiei”, DAN SSSR, 139:2 (1961), 309–312 | Zbl

[3] A. D. Yashin, “New intuitionistic logical constants and Novikov completeness”, Stud. Log., 63:2 (1999), 151–180 | DOI | MR | Zbl

[4] A. D. Yashin, “O novoi konstante v intuitsionistskoi logike vyskazyvanii”, Fund. i prikl. matem., 5:3 (1999), 903–926 | MR | Zbl

[5] A. D. Yashin, “Kontinualnost semeistva polnykh po Novikovu logik s novoi odnomestnoi svyazkoi”, Vestnik MGU, ser. 1, matem., mekhan., 1997, no. 3, 22–25 | MR | Zbl

[6] A. Chagrov, M. Zakharyaschev, Modal Logics, Oxford Logic Guides, 35, Clarendon Press, Oxford, 1997 | MR | Zbl

[7] E. Raseva, R. Sikorskii, Matematika metamatematiki, Nauka, M., 1972 | MR

[8] L. L. Esakia, Algebry Geitinga, Metsniereba, Tbilisi, 1985 | MR | Zbl

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

[10] D. P. Skvortsov, “Ob intuitsionistskom ischislenii vyskazyvanii s dopolnitelnoi logicheskoi svyazkoi”, Issledovaniya po neklassicheskim logikam i formalnym sistemam, Nauka, M., 1983, 154–173 | MR

[11] R. Sh. Grigoliya, “Svobodnye $S4.3$-algebry s konechnym chislom obrazuyuschikh”, Issledovaniya po neklassicheskim logikam i formalnym sistemam, Nauka, M., 1983, 281–287 | MR

[12] V. V. Rybakov, Admissibility of logical inference rules, Stud. Logic Found. Math., 136, Elsevier Science B.V., Amsterdam–New York, 1997 | MR | Zbl