Cambridge Summer School In Mathematical Logic by A. R. D. Mathias, H. Rogers

By A. R. D. Mathias, H. Rogers

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E k) on the s t r e n g t h of a 0 , . . , ~ k be able of just an initial how we c o n t i n u e and A ( ~ , ~ 0 , . . , e k ) . As ~ develops segment lawless as follows: of our k n o w l e d g e case one r e a s o n s the v a l i d i t y is a r g u e d it is i r r e l e v a n t that no i n f o r m a t i o n regardless in in its be able to of a finite develops initial free- segment n A ( ~ , ~ 0 , . . , ~ k) must hold. The i m p o r t a n c e following B 3 n ( ~ • n ^ V6 • n A(~)). ,~k) generation.

Conclude K V~ R ( e , e ( ~ ) ) . 5. Choice sequences Between lawless notions of c h o i c e exposition sequences of the to [ T r o e l s t r a , [Troelstra, sequence general 69A], 69]. We will values, forwardly be g e n e r a l i z e d idea b e h i n d numbers process can be d e s c r i b e d numbers and conditions. (for the we ~,~ E (N)N). successive [Brouwer, between let one is r e f e r r e d to choice is that straight- successively future (x,R> restrict t h e m to be e x t e n s i o n a l , with sequences.

LS1Vx LSI states The v a r i a b l e s (~ e can be e x t e n d e d on the ~ ~ 6 of this intended v ~ ~ intensional interpretation. g. only denote they Note that available object LS1 is not evident one cheats finite a given f i n i t e LS3 ~ of a die). sequences e i t h e r we know b e f o r e h a n d for s e q u e n c e s of throws. sequence denote of n u m b e r s case if A(~) to c o n c l u d e segment In the the sense conclude ly, A(~) produced by a a to t h i n k of pro- by use of a die. case ^ e ~ ~k" ~ A(B,a0,-'',ak)) parameter t h e n we must that segment.

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