[FOM] Query on nonstandard models of the integers

A J Franco de Oliveira francoli at kqnet.pt
Tue Nov 6 14:36:25 EST 2007

There is one trivial answer, which may not be what you are looking for.
The answer is yes, in E. Nelson's IST (Internal Set Theory: A new 
approach to Non Standard Analysis. Bull. Amer. Math. Soc. 83 (1977), 
1165-1198), which is a conservative extension of ZFC, with a new 
predicate (to be standard) and axioms that imply the existence of 
nonstandard elements in every infinite set. In this theory, 
therefore, the set of integers has non-standard (infinitely large) 
elements, but the property in question is a standard property, so it 
holds for all integers, standard and nonstandard. A prime 
decomposition of an infinite integer has, however, a nonstandard 
number of factors.

At 04:31 04-11-2007, you wrote:
>Is there any nonstandard model of the integers which has the unique
>factorization property?
>-- JS
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