Simplified Models Establishing some of Né:zondet's Results on Erdös–Woods Conjecture

Author: Guillaume, M.

Source: Synthese, Volume 125, Numbers 1-2, January 2000 , pp. 133-146(14)

Publisher: Springer

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Abstract:

The first step of the construction of Nézondet's models of finite arithmetics which are counter-models to Erdös–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.

Document Type: Regular Paper

Affiliations: Universiteacute; Blaise Pascal (Clermont-Ferrand II) and Laboratoire de Logique, Algorithmique et Informatique Université d'Auvergne (Clermont-Ferrand I) France E-mail: guill@llaic.u-clermont1.fr

Publication date: January 1, 2000

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