The degrees of maximality of the intuitionistic propositional logic and of some of its fragments

Abstract

Professor Ryszard Wojcicki once asked whether the degree of maximality of the consequence operationC determined by the theorems of the intuitionistic propositional logic and the detachment rule for the implication connective is equal to $$2^{2^\aleph 0} $$ ? The aim of the present paper is to give the affirmative answer to the question. More exactly, it is proved here that the degree of maximality ofC Ψ — theΨ — fragment ofC, is equal to $$2^{2^\aleph 0} $$ , for every such that → eΨ.