# [FOM] Query on nonstandard models of the integers

Gyorgy Sereny sereny at math.bme.hu
Sun Nov 4 18:08:06 EST 2007


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

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