[FOM] Query on nonstandard models of the integers

[Gyorgy Sereny]

On Sun, 4 Nov 2007, joeshipman at aol.com wrote:

> Is there any nonstandard model of the integers which has the unique
> factorization property?


Donald Monk's remarks on page 344 of his book
`Mathematical Logic' may be relevant:

   ... there are nonstandard numbers cannot be written
   as a finite product of primes. An interesting example is
   <2^n : n \in \omega >/F, which is divisible only
   by the prime 2, but is not a (finite) power of 2.


Gyorgy Sereny