A sheaf-theoretic foundation for nonstandard analysis
type: Item
instance of: scholarly article
title: A sheaf-theoretic foundation for nonstandard analysis
zbMATH Open document ID: 0880.03032
DOI: 10.1016/S0168-0072(96)00041-3
author: Erik Palmgren
published in: Annals of Pure and Applied Logic
publication date: 1998-01-28T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 03F60
Mathematics Subject Classification ID: 03H15
Mathematics Subject Classification ID: 03H05
zbMATH DE Number: 1022204
zbMATH Keywords: constructive nonstandard analysis
zbMATH Keywords: extension of a sheaf-theoretic model
zbMATH Keywords: nonstandard arithmetic
zbMATH Keywords: uniform continuity
zbMATH Keywords: differentiability
zbMATH Keywords: order type of the nonstandard natural numbers
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1022204