Geodesic
Perceptibility in pre-Heyting logics
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1064-1072.

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This paper is dedicated to problems of perceptibility and recognizability in pre-Heyting logics, that is, in extensions of the minimal logic J satisfying the axiom $\neg\neg (\bot\rightarrow p)$. These concepts were introduced in [8, 11, 10]. The logic Od and its extensions were studied in [5, 14] and other papers. The semantic characterization of the logic Od and its completeness were obtained in [5]. The formula F and the logic JF were studied in [12]. It was proved that the logic JF has disjunctive and finite-model properties. The logic JF has Craig's interpolation property (established in [17]). The perceptibility of the formula F in well-composed logics is proved in [14]. It is unknown whether the formula F is perceptible over J [8]. We will prove that the formula F is perceptible over the minimal pre-Heyting logic Od and the logic OdF is recognizable over Od.
Keywords: Recognizability, perceptibility, minimal logic, pre-Heyting logic, superintuitionistic logic
Mots-clés : Johansson algebra, Heyting algebra, calculus. 
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L. L. Maksimova; V. F. Yun. Perceptibility in pre-Heyting logics. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 1064-1072. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a26/

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