By Joseph R. Shoenfield (Eds.)
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Extra resources for Degrees of Unsolvability
Then x E A f S 3y(
And t a k e A to b e t h e unique s e t such However, t h e t r e e s a r e t r e a t e d d i f f e r - A t s t e p s , we d e f i n e t r e e s T ently. For i n o t be t o t a l ) . < S i for i 5 ks (which need S ks, Tf+l w i l l b e a s u b t r e e of T:; S S 6, w i l l b e on Tk is and hence on a l l t h e T i . and W e w i l l always S have Tg = I d . A t t h e end of t h e c o n s t r u c t i o n , we show t h a t converges i n a s u i t a b l e s e n s e t o a t r e e Ti. T! Now we d e s c r i b e s t e p s .
Any such I i s t h e n c a l l e d an i n d e x of A . Parameter Theorem. If A i s a n RE r e l a t i o n i n X X Y, t h e n 22 FZCURSIVE ENUMERABILITY t h e r e i s a r e c u r s i v e f u n c t i o n F from Y t o Alg(X,N) such t h a t X € WF(y)@ A