FOM: What is the standard model for PA?

[Martin Davis]

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