Logic

Aspects of Mathematical Logic by H. Hermes (auth.), Prof. E. Casari (eds.)

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

H. Hermes: simple notions and purposes of the idea 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 final conception of semisets. Syntactic versions of the set theory.

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Hypothesis: F o r every infinite cardinal n the number an is the f i r s t inaccessible cardinal > n (I1 P e r ogni numero cardinale infin nito n, 2 6 il primo numero' inaccessibile >nn) . 1. ) was introduced in 1937 (cf. Kurepa C157 , formula (2)) . ) is implied by the axiom of choi- ce; probabljr ,the converse holds too. 4. Here is a s e r i e s of nice continuum hypotheses. then f o r every ordinal q (the case n = l yields the Cantor's 3'. 5. A general continuum hypothesis) one has . ,great variety of continuum hypotheses is obtained in the D.

Solution of P o s t ' s Reduction P r o b l e m and S o m e O t h e r P r o b l e m s of t h e ' T h e o r y of A l g o r i t h m s I. A m e r . M a t l ~ . Soc. T r a n s l a t i o n s (2) 2 (1963), 197-215. P e t e r , R. R e k u r s i v e Funktionen. A k a d e m i e - V e r l a g , B e r l i n (21957). 278 pp. P e t e r , R. Uber die Verallgemeinerung d e r Theorie d e r redurs i v e n Funktionen f u r a b s t r a k t e Mengen g e e i g n e t e r S t r u k t u r a l s Definitionsbereiche. Acta Math.

4 - Let be ... a . ; q a n a r b i t r a r y configuration (where a a is o n o 1 "' t h e i n s c r i p t i o n , n . t h e n u m b e r of t h e s c a n n e d s q u a r e a n d q t h e s t a t e ) . Let be C = a Now we define ( ( 7 . ) Now a l l t h e c o n d i t i o n s a r e s a t i - s f i e d : In t h e c o r n e r we h a v e d o m i n o (K). E v e r y s t r i p satisfies the hori- z o n t a l m a t c h i n g condition. T h a t a l s o t h e t h e v e r t i c a l m a t c h i n g condition i s s a t i s f i e d m u s t b e shown f o r S .

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