Summary: 1. Recursive functions.
For each n N we let
Nn
be {} if n = 0 and we let it be the set of n-tuples (x1, . . . , xn) where xi N for
i {1, . . . , n}. For m, n N we let
Nn
m
be the set of f such that f : Nn
Nm
.
Note that
N0
m f f() Nm
is univalent with range Nm
; in what follows we shall identify N0
m with Nm
via this
mapping.
Definition 1.1. Suppose A Nn
. We define