AN ALGEBRAIC PROOF OF THE SEPARATION PROPERTY FOR AN INTUITIONISTIC PROVABILITY CALCULUS
A. Yu. Muravitskii · Mathematics of the USSR-Sbornik · 1988
For intuitionistic provability calculus obtained from the intuitionistic propositional calculus by adjoining to the postulates of the latter the axioms , , and , an algebraic proof is given of the separation property: if and only if there exists a derivation of formula whose terms contain only those connectives that occur in . The proof is achieved by constructing an (isomorphic) embedding of pseudo-Boolean algebras, and on this basis then constructing embeddings, into -pseudo-Boolean algebras, of algebras whose classes approximate corresponding fragments of the calculus .Bibliography: 14 titles.