A sheaf-theoretic foundation for nonstandard analysis
The author presents a new foundation for constructive nonstandard analysis. It is an extension of a sheaf-theoretic model of nonstandard arithmetic due to I. Moerdijk. The model is composed of representable sheaves over a site of filter bases. Certain well-known basic nonstandard characterizations for such concepts as uniform continuity and differentiability are obtained. Within this model, it is shown that the order type of the nonstandard natural numbers is the same as in the classical case.
order type of the nonstandard natural numbers
scientific article; zbMATH DE number 1022204