FOM: Re: infinity of the universe

[Ara R. Aslyan]

This is my comments to Randall Holmes following message:
>
> Dear All,
>
> If the universe is infinite then there are enough objects to
> support an interpretation of the mathematics of the natural numbers
> (and arguably also of the reals) in which each object we are commmitted
> to is a physical object.

Actually the infinite universe is far from being enough for number theory
interpretation, since the former consists not only from natural numbers but
also roughly speaking from claims stated and proved concerning natural
numbers i.e. number theory itself. As an example we may take Presburger's
arithmetic's which is proved to be consistent and having an infinite model
but the amount of number theory provable in this formal system is far from
being satisfactory.

Regards,

Ara Aslyan.