Re: Partial recursive functions and minimization

O/H Twoflower ??????:
Hi all,

let's have partial recursive function F, which is not recursive. I
don't understand, why

G(x) = Min(y) (F(x,y) = 0)

(where Min(y) is just minimization operator or unrestricted mu-
recursion)

is not partial recursive function.

Could someone please explain this to me?

Thank you very much.

I don't understand the question.
The Kleene operator together with primitive recursive defines the set of recursive functions. So, if F is primitive recursive, then yes, G is not primitive recursive, but only recursive. But if F is only partial recursive then I don't see why G should not be partial recursive too.
.

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