Science Talk

Dick · Guest

I am trying to understand computability by reading "Computability
Theory" by Cooper. I am stuck on the concept of Creative Set.
A creative set, A is defined as:-
A is creative if
1. A is c.e.
2. There exists f(e) s.t.
W(e) belongs ^A => f(e) belongs ^A-W(e)

K = {e st e belongs W(e) is given as an example with creative function
f(x) = x
It is stated that naturally occurring non computable sets ar usually
creative.

Is K(k) = { W(e) st (k belongs to W(e)} creative?
The creative function should be f(e) = k. However for some values of
k , { k belongs W(K) and so f(k) belongs K(k) and the set is not
creative.

What have I misunderstood?
Can you give an example of a creative set with creative function
different from f(x) = x?

Dick Batchelor