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Algebraic proof of the separation property for an intuitionistic provability calculus
Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 397-406 Cet article a éte moissonné depuis la source Math-Net.Ru

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For intuitionistic provability calculus $I^\Delta$ obtained from the intuitionistic propositional calculus by adjoining to the postulates of the latter the axioms $(p\supset\Delta p)$, $((\Delta p\supset p)\supset p)$ and $(\Delta p\supset(((q\supset p)\supset q)\supset q))$, an algebraic proof is given of the separation property: $I^\Delta\vdash a$ if and only if there exists a derivation of formula $a$ whose terms contain only those connectives that occur in $a$. The proof is achieved by constructing an (isomorphic) embedding of pseudo-Boolean algebras, and on this basis then constructing embeddings, into $\Delta$-pseudo-Boolean algebras, of algebras whose classes approximate corresponding fragments of the calculus $I^\Delta$. Bibliography: 14 titles. 
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     title = {Algebraic proof of the separation property for an intuitionistic provability calculus},
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A. U. Muravitskii. Algebraic proof of the separation property for an intuitionistic provability calculus. Sbornik. Mathematics, Tome 59 (1988) no. 2, pp. 397-406. http://geodesic.mathdoc.fr/item/SM_1988_59_2_a7/

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