Simplified models establishing some of Nezondet's results on Erdos-Woods conjecture

The first step of the construction of Nezondet's models of finite arithmeti cs which are counter-models to Erdos-Woods conjecture is to add to the natu ral numbers the non-standard numbers generated by one of them, using additi on, multiplication and divisions by a natural factor allowed in an ultrapow er 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 Chin ese remainder's theorem, so that a model as desired is obtained as early as at the first time.