FOM: What is the standard model for PA?
Martin Davis
martind at cs.berkeley.edu
Wed Mar 25 15:04:45 EST 1998
At 06:40 PM 3/25/98 +0300, sazonov at logic.botik.ru wrote:
>In the light of discussion on feasible numbers (and also in a
>general context) I have a question to everybody.
>
>What makes the powerset 2^N of natural numbers (i.e. the set of
>infinite binary strings) to be indeterminate *in contrast to*
>the powerset 2^1000={0,1}^1000 of {1,2,...1000} which should be
>determinate (according to the traditional view and *contrary* to
>my intuition)? What is the crucial difference? Is this
>difference based on *infinity* of N and in *finity* of
>{1,2,...1000}? Note, that 2^1000 (as well as 2^N) behaves now
>*as an infinity* from the point of view of feasibility. I
>believe that comparison would be interesting.
>
Indeed a good question. My answer would be that both are perfectly determinate.
Martin
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