Geodesic
Calculi over minimal logic and nonembeddability of algebras
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 704-715

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Algebraic semantics of the minimal logic $\mathrm{J}$ is constructed by using Johansson algebras ($\mathrm{J}$-algebras). In this paper the description of Heyting algebras in terms of nonembeddability of $\mathrm{J}$-algebras was found. As a corollary the characterization of superintuitionistic, wellcomposed and some other calculi in the class of various calculi over $\mathrm{J}$ was found. The central role is played by a special $\mathrm{J}$-algebra $M_{0,\omega}$, constructed and described in this paper.
Keywords: Minimal logic, superintuitionistic logic
Mots-clés : Johansson algebra, Heyting algebra, calculus. 
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     author = {L. L. Maksimova and V. F. Yun},
     title = {Calculi over minimal logic and nonembeddability of algebras},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {704--715},
     publisher = {mathdoc},
     volume = {13},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2016_13_a18/}
}
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L. L. Maksimova; V. F. Yun. Calculi over minimal logic and nonembeddability of algebras. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 13 (2016), pp. 704-715. http://geodesic.mathdoc.fr/item/SEMR_2016_13_a18/