Abstract

This paper is a sequel to my [7]. It focuses on the notion of natural number as introduced in section 11 of that paper with regard to forms of induction and recursive definitions. One point is that this notion of natural number is somewhat weaker than the classical one in so far as it is defined in terms of a weak implication. The other point is the lack of even a weak form of extensionality. As a main result of the present paper it will turn out that the means provided in [7] are sufficient to account for an interpretation of primitive recursive arithmetic