Pretabularity and Craig's interpolation problem over the minimal logic
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 245-250.

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In this paper [1] the tabularity problem was solved and all pre-tabular extensions of the minimal logic were described. In total, there turned out to be seven pre-tabular logics over the minimal logic. In this article, we will prove that four of them have the Craig's interpolation property CIP and two do not have. The question of CIP in the seventh logic is still open.
Keywords: minimal logic, tabularity, pre-tabular logic
Mots-clés : interpolation problem.
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L. L. Maksimova; V. F. Yun. Pretabularity and Craig's interpolation problem over the minimal logic. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 1, pp. 245-250. http://geodesic.mathdoc.fr/item/SEMR_2023_20_1_a7/

[1] L.L. Maksimova, V.F.Yun, “The tabularity problem over the minimal logic”, Sib. Math. J., 57:6 (2016), 1034–1043 | DOI | MR | Zbl

[2] I. Johansson, “Der Minimalkalkül, ein reduzierter intuitionistischer Formalismus”, Compositio Math., 4 (1936), 119–136 | MR | Zbl

[3] W. Craig, “Three uses of Herbrand-Gentzen theorem in relating model theory”, J. Symb. Log., 22 (1957), 269–285 | DOI | MR | Zbl

[4] L.L. Maksimova, “Craig's theorem in superintuitionistic logics and amalgamable varieties of pseudoboolean algebras”, Algebra Logika, 16:6 (1977), 643–681 | DOI | MR | Zbl

[5] L.L. Maksimova, V.F. Yun, “Layers over minimal logic”, Algebra Logic, 55:4 (2016), 295–305 | DOI | MR | Zbl

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

[7] L.L. Maksimova, “Craig's interpolation theorem and amalgamable varieties”, Sov. Math., Dokl., 18 (1978), 1550–1553 | MR | Zbl

[8] D.M. Gabbay, L. Maksimova, Interpolation and definability. Modal and intuitionistic logics, Clarendon Press, Oxford, 2005 | MR | Zbl

[9] W. Rautenberg, Klassische und nichtklassische Aussagenlogik, Friedr. Vieweg Sohn, Braunschweig/Wiesbaden, 1979 | MR | Zbl

[10] A.I. Mal'cev, Algebraic systems, Akademie-Verlag, Berlin, 1973 | MR | Zbl

[11] S. Odintsov, Constructive negations and paraconsistency, Trends in Logic-Studia Logica Library, 26, Springer, Dordrecht, 2008 | MR | Zbl

[12] L.L. Maksimova, “Implicit definability and positive logics”, Algebra Logic, 42:1 (2003), 37–53 | DOI | MR | Zbl

[13] L. Maksimova, “Interpolation and definability over the logic Gl”, Stud. Log., 99:1-3 (2011), 249–267 | DOI | MR | Zbl

[14] L.L. Maksimova, “Interpolation and definability in extensions of the minimal logic”, Algebra Logic, 44:6 (2005), 407–421 | DOI | MR | Zbl

[15] S. Odintsov, “Logic of classic refutability and class of extensions of minimal logic”, Log. Log. Philos., 9 (2001), 91–107 | DOI | MR | Zbl