On admissible rules of intuitionistic propositional logic

This paper studies modus rules of deduction admissible in intuitionistic propositional logic (a rule is called a modus rule if it corresponds to some sequence and allows passage from the results of any substitution in the formulas in its antecedent to the result of the same substitution in its succedent). Examples of such rules are considered, as well as the derivability of certain rules from others by means of the intuitionistic propositional calculus. An infinite independent system of admissible modus rules is constructed. It is proved that a finite Gödel pseudo-Boolean algebra in which all modus rules are valid (i.e. the quasi-identities corresponding to them are valid) is isomorphic to a sequential union of Boolean algebras of power not greater than 4.
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