Abstract
In this chapter we treat the theory of functionals of finite type in which, following K Gödel [2] pure number theory can be interpreted (§19). The functionals concerned are introduced in §15 and they are shown to be calculable in §16 following W. Howard by transfinite induction up to εε0, in fact, by using the ordinal terms of §14. In §17 we develop a formal system on the basis of the positive implicational calculus (with equality) as a logical setting for the theory of functiorrals of finite type.
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