Synthese 125 (1-2):133 - 146 (2000)

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.
Keywords Philosophy   Philosophy   Epistemology   Logic   Metaphysics   Philosophy of Language
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Reprint years 2004
DOI 10.1023/A:1005227515270
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