A deduction theorem for restricted generality.

Abstract

In this paper, a deduction theorem for restricted generality () will be proved on the basis of a finite number of axioms which do not contain variables. The theorem is in such a form as to avoid both Curry's paradox 1 and the Kleene Rosser paradox. 2 In fact it can be shown that nothing inconsistent can be proved using this form of the deduction theorem and the basic rules given below. 3 An iterated form of the theorem can also be derived, as well as deduction theorems for P (implication) and (universal generality).