A constructive approach to nonstandard analysis
type: Item
instance of: scholarly article
title: A constructive approach to nonstandard analysis
zbMATH Open document ID: 0830.03037
DOI: 10.1016/0168-0072(94)00030-7
author: Erik Palmgren
published in: Annals of Pure and Applied Logic
publication date: 1995-07-03T00:00:00Z
review text: The author introduces a constructive theory that may be useful in developing some of the areas of elementary nonstandard analysis. The theory is a conservative extension of \(\mathbf {HA}^\omega+ \mathbf {AC}\). The author adjoins a predicate, much as is done in Nelson's internal set theory, that distinguishes standard objects. A weak transfer and an idealisation principle are then proved from his axioms. The author illustrates the use of this approach by establishing some of the elementary nonstandard statements relating the hyperreals, infinitesimals, and the usual concepts one associates with elementary real analysis. Of course, this approach is weaker than the customary Robinson methods.
Mathematics Subject Classification ID: 03H05
Mathematics Subject Classification ID: 26E35
Mathematics Subject Classification ID: 03F65
zbMATH DE Number: 768745
zbMATH Keywords: internal set theory
zbMATH Keywords: hyperreals
zbMATH Keywords: infinitesimals
MaRDI profile type: Publication
full work available at URL: 0168-0072(94)00030-7
OpenAlex ID: W2127548353
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description: scientific article; zbMATH DE number 768745