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

Professor Ryszard Wójcicki 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 → εΨ.