A sheaf-theoretic foundation for nonstandard analysis (Q1356978)
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scientific article; zbMATH DE number 1022204
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A sheaf-theoretic foundation for nonstandard analysis |
scientific article; zbMATH DE number 1022204 |
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A sheaf-theoretic foundation for nonstandard analysis (English)
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28 January 1998
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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.
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constructive nonstandard analysis
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extension of a sheaf-theoretic model
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nonstandard arithmetic
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uniform continuity
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differentiability
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order type of the nonstandard natural numbers
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