Abstract
The first step of the construction of Nezondet's models of finite arithmetics which are counter-models to Erdos–Woods conjecture is to add to the natural numbers the non-standard numbers generated by one of them, using addition, multiplication and divisions by a natural factor allowed in an ultrapower construction. After a review of some properties of such a structure, we show that the choice of the ultrafilter can be managed, using just the Chinese remainder's theorem, so that a model as desired is obtained as early as at the first time.
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