By H. Hermes (auth.), Prof. E. Casari (eds.)

H. Hermes: simple notions and functions of the speculation of decidability.- D. Kurepa: On numerous continuum hypotheses.- A. Mostowski: types of set theory.- A. Robinson: difficulties and strategies of version theory.- S. Sochor, B. Balcar: the final thought of semisets. Syntactic types of the set theory.

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We t h e r e f o r e h a v e (s)+l. That gives E ( s ) = 0, C a s e 1. Hene ( s ) = e and by ( 5 . 9 ) where ber y r ( s ) i s determin2d a s in ( 5 . 9 ) . A c c o r d i n g t o (*) we h a v e a num- s. t. ther fO: In L e c t u r e 3 , no. 2 we h a v e m e n t i o n e d T 1 zxy holds o r n ~ t ,we h a v e l o a s k t h e g o r a c l e f o r g only f o r a r g u m e n t s which a r e l e s s t h a n y . In o u r c a s e we y < s . H e n c e i t i s sufficient t o show t h a t m e values for each x

L. R e c u r s i v e l y E n u m e r a b l e S e t s of P o s i t i v e I n t e g e r s and t h e i r D e c i s i o n P r o b l e m s . Bull A m e r Math. Soc. 5 0 (1944), 284-316. . Ritchie, D. M. Complexity Classification of P r i m i t i v e R e c u r s i v e F u n c t i o n s b y t h e i r Machine P r o g r a m s . Notices of t h e A m e r . Math. Soc. 2 (1965), 343. Ritchie, R. W. C l a s s e s of p r e d i c t a b l y C o m p u t a b l e F u n c t i o n s . T r a n s a c t i o n s A m e r .

2. Let be given a class ble property J'A is associated in an effective way, (Qs i s satisfiable. s. t. H. Hermes theorem that satisfiability i s unde- This would be a proof of Church's cidable. Furthermore it could be that for every s a subclass A of the c l a s s of a l l formulae. 1) the theorem that a l s o for A In the following we domino s e t s D, and P 0 D, D choose 0 where D O_ has exactly one element and i s included in a s the property of beidg good for the origin-restricted c a s e , In shown that is undecidable.