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

H. Hermes: simple notions and purposes of the speculation of decidability.- D. Kurepa: On a number of continuum hypotheses.- A. Mostowski: types of set theory.- A. Robinson: difficulties and strategies of version theory.- S. Sochor, B. Balcar: the overall concept of semisets. Syntactic types of the set theory.

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Wang Entscheidungsproblem reduced to the V w ~ a s e . P r o c . Nat. A c a d . S c i USA 4 8 (1962), 365-377. Kleene, S. C. 1 I n t r o d u c t i o n t o M e t a m a t h e m a t i c s . North-Holland P u b l i s h i n g C o . , A m s t e r d a m (41964). X+550 p p . Kleene, S. C. 2 M a t h e m a t i c a l L o g i c . John Wiley a n d Sons, New Y o r k (1967). XI11398 pp. K l e e n e , S. C. a n d E . L . P o s t 1 T h e U p p e r S e m i - L a t t i c e of D e g r e e s of R e c u r s i v e Unsolvability.

5. -.. The formula we s e e If i n ( 8 . 8 ) we i n t e r c h a n g e Y D , DO i m m e d i a t e l y t h a t t h e r e is a q u a n t o r - f r e e f o r m u l a exactly three f r e e variables (where 'Ix) U x, u, y, s. t . is a s u b s t i t u t i o n o p e r a t o r ) TD,DO . Now x and y with D, DO is equivalent t o it is a well-known f a c t ("Skolem f u n c t i o n s f f )t h a t (8. 14) is s a t i s f i a b l e if a n d o n l y if is s a t i s f i a b l e . (8. 15) c u l u s . We identify (8.

1) a TM We. Hence Mo, s . t . F o r every M: M 0 ' applied on G(M), halts iff M, applied on G(M), does not halt. This leads immediately to a contradiction for M = Mo . 3. Domino problems. A domino is an oriented square plate with colors on each edge. A d ~ m i n omust not be rotated o r reflected. Two dominoes a r e of the s a m e --type if the corresponding edges have the s a m e colors. (We sometimes confound dominoes with their types). Let be given a finite s e t D D i s called -good if it i s possible of domino types.