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Approaches to analysis with infinitesimals following Robinson, Nelson, and others

Fletcher, Peter; Hrbacek, Karel; Kanovei, Vladimir; Katz, Mikhail G.; Lobry, Claude; Sanders, Sam

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Authors

Karel Hrbacek

Vladimir Kanovei

Mikhail G. Katz

Claude Lobry

Sam Sanders



Abstract

This is a survey of several approaches to the framework for working with infinitesimals and infinite numbers, originally developed by Abraham Robinson in the 1960s, and their constructive engagement with the Cantor-Dedekind postulate and the Intended Interpretation hypothesis. We highlight some applications including (1) Loeb's approach to the Lebesgue measure, (2) a radically elementary approach to the vibrating string, (3) true infinitesimal differential geometry. We explore the relation of Robinson's and related frameworks to the multiverse view as developed by Hamkins. Keywords: axiomatisations, infinitesimal, nonstandard analysis, ultraproducts, superstructure, set-theoretic foundations, multiverse, naive integers, intuitionism, soritical properties, ideal elements, protozoa.

Journal Article Type Article
Acceptance Date Oct 28, 2016
Publication Date Nov 3, 2017
Publicly Available Date Mar 28, 2024
Journal Real Analysis Exchange
Print ISSN 0147-1937
Peer Reviewed Peer Reviewed
Pages 1 -59
DOI https://doi.org/10.14321/realanalexch.42.2.0193
Publisher URL https://www.jstor.org/stable/10.14321/realanalexch.42.2.0193
Related Public URLs https://arxiv.org/abs/1703.00425

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