Restricted interpolation property in superintuitionistic logics

L. L. Maksimova

Algebra i logika, Tome 48 (2009) no. 1, pp. 54-89.

Résumé

The restricted interpolation property IPR in modal and superintuitionistic logics is investigated. It is proved that in superintuitionistic logics of finite slices and in finite-slice extensions of the Grzegorczyk logic, the property IPR is equivalent to the projective Beth property PB2.

Détail

Keywords: restricted interpolation property, projective Beth property, superintuitionistic logic, Grzegorczyk logic.

Bibliographie

[1] L. L. Maksimova, “Proektivnye svoistva Beta v modalnykh i superintuitsionistskikh logikakh”, Algebra i logika, 38:3 (1999), 316–333 | MR | Zbl

[2] L. L. Maksimova, “Superintuitsionistskie logiki i proektivnoe svoistvo Beta”, Algebra i logika, 38:6 (1999), 680–696 | MR | Zbl

[3] L. Maksimova, “Intuitionistic logic and implicit definability”, Ann. Pure Appl. Logic, 105:1–3 (2000), 83–102 | DOI | MR | Zbl

[4] L. L. Maksimova, “Neyavnaya opredelimost i pozitivnye logiki”, Algebra i logika, 42:1 (2003), 65–93 | MR | Zbl

[5] L. L. Maksimova, “Opredelimost v normalnykh rasshireniyakh logiki S4”, Algebra i logika, 43:4 (2004), 387–410 | MR | Zbl

[6] D. M. Gabbay, L. Maksimova, Interpolation and definability. Modal and intuitionistic logics, Oxford Logic Guides, 46, Clarendon Press, Oxford University Press, Oxford, 2005 | MR | Zbl

[7] L. L. Maksimova, “Razreshimost proektivnogo svoistva Beta v mnogoobraziyakh geitingovykh algebr”, Algebra i logika, 40:3 (2001), 290–301 | MR | Zbl

[8] L. Maksimova, “Projective Beth property in extensions of Grzegorczyk logic”, Stud. Log., 83:1–3 (2006), 365–391 | DOI | MR | Zbl

[9] L. L. Maksimova, “Proektivnoe svoistvo Beta i interpolyatsiya v pozitivnykh i blizkikh k nim logikakh”, Algebra i logika, 45:1 (2006), 85–113 | MR | Zbl

[10] L. Maksimova, “Restricted interpolation in modal logics”, Advances in modal logic, Vol. 4, eds. Ph. Balbiani et al., King's College Publ., London, 2003, 297–311 | MR | Zbl

[11] H. Rasiowa, R. Sikorski, The mathematics of metamathematics, PWN, Warszawa, 1963 | MR

[12] W. Blok, Varieties of interior algebras, PhD Thesis, Univ. Amsterdam, 1976

[13] T. Hosoi, “On intermediate logic. I”, J. Fac. Sci. Univ. Tokyo Sec. Ia, 14 (1967), 293–312 | MR

[14] L. L. Maksimova, “Teorema Kreiga v superintuitsionistskikh logikakh i amalgamiruemye mnogoobraziya psevdobulevykh algebr”, Algebra i logika, 16:6 (1977), 643–681 | MR | Zbl

[15] L. L. Maksimova, “Modalnye logiki i mnogoobraziya modalnykh algebr: svoistvo Beta, interpolyatsiya i amalgamiruemost”, Algebra i logika, 31:2 (1992), 145–166 | MR | Zbl

[16] L. L. Maksimova, “Ogranichennaya interpolyatsiya i proektivnoe svoistvo Beta v ekvatsionalnoi logike”, Algebra i logika, 42:6 (2003), 712–726 | MR

[17] L. L. Maksimova, V. V. Rybakov, “O reshëtke normalnykh modalnykh logik”, Algebra i logika, 13:2 (1974), 188–216 | MR | Zbl

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

[19] L. L. Maksimova, “Projective Beth's properties in infinite slice extensions of the modal logic K4”, Advances in modal logic, Vol. 3, eds. F. Wolter et al., World Sci. Publ., Singapore, 2002, 349–363 | MR | Zbl