41. The preimage of a recursively enumerable set under a partial recursive function is a recursively enumerable set. 42. Defining primitive recursive functions in this manner is not possible in PRA, because it lacks quantifiers. 43. Let \ mathcal { C } be a class of partial recursive functions with index set C. 44. Primitive recursive functions tend to correspond very closely with our intuition of what a computable function must be. 45. :Let \ mathcal { C } be a class of partial recursive functions with index set C. 46. Functional interpretations have also been used to provide ordinal analyses of theories and classify their provably recursive functions . 47. Her final book, published in 1976, was " Recursive Functions in Computer Theory ". 48. :Are you using " recursive function " in the computer science sense of the term? 49. We want a constructive and algorithmic connection : a ( total ) recursive function that performs the encoding. 50. This can sometimes be done more elegantly via mutually recursive functions ; the SierpiDski curve is a good example.
