By J N Crossley (auth.), Prof. John Newsome Crossley (eds.)

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Extra info for Algebra and Logic: Papers from the 1974 Summer Research Institute of the Australian Mathematical Society, Monash University, Australia

Example text

The whole a calculation. in fact behave National as you know, Physical solution circuitry In all these ways If it was a q u e s t i o n would in the in practice, calculations he d e s i g n e d Laboratory of w a n t i n g as well. the c o m p u t e r in work, that he p r o b l e m and never ran away then do all the n u m e r i c a l of course, to help all the electric and he not only, did a lot of t h e o r e t i c a l designed you immense our w o r k during the war, always it you did not know any- to tackle from first principles.

No, but you know, very useful theorems, for instance, I could r e c o n s t r u c t all the proofs which G~del had about c o n s e q u e n c e s of V = L, for d e s c r i p t i v e set theory. These were l a t e r ' p u b l i s h e d by A d d i s o n Novikoff (Novikoff [51]). (Addison [59]) and But I had it already then and I had also the d e c i d a b i l i t y of the e l e m e n t a r y theory of well-ordering. There is an abstract of Tarski and m y s e l f about it (Mostowski and Tarski [49]), but the proof was never p u b l i s h e d because the procedure of eliminating quantifiers was hard and required too many details to be w o r k e d out, and I had this all w r i t t e n up there, Nerode I regret that.

Result ... You know there paper of Skolem w h i c h has a very long name: suchungen [ber ProduktationsKlassen die Axiome und That Mostowski In effect he proves betreffen". That is a "Unter- des K l a s s e n k a l k u l s Summationsprobleme, von A u s s a g e n Sacks of und [ber welche gewisse is the title. is a title: predicate individual calculus there that, with variables if you have quantifiers unary not only for but for f u n c t i o n a l variables, then 25 this gives you a d e c i d a b l e Sacks What is that, Mostowski Yes, second Sacks I did not k n o w that was his Mostowski There he uses Keisler What Mostowski The year Sacks 1919!

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