ABSTRACT
The results of the last section can be relativized to a class Φ of total functions of number variables. A particularly interesting case is that in which Φ 75is the class of all such functions. Replacing the functions by their contractions, we see we are relativizing to the class ℝ of reals. Note that by 18.1, a function is recursive in ℝ iff it is obtained from a recursive function by replacing some of the unary function variables by names of particular reals. The same then holds with recursive replaced by Π k 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203741139/8e9d6847-fedd-45bc-9ee6-91ac5be8d222/content/in73_14.tif"/> or Σ k 1 https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203741139/8e9d6847-fedd-45bc-9ee6-91ac5be8d222/content/in73_15.tif"/> .
