The independence of connectives

Abstract

In a paper in this J ournal [1], McKinsey used as a criterion for the independence (non-definability) of a connective F in a propositional calculus L , the existence of a matrix for L in which the functions corresponding to all the connectives other than F are class-closing over some subset S of the elements, while the function corresponding to F is not class-closing over S (i.e., for a certain choice of arguments in S its value is not in S ).