Open Access
2017 Approaches to Analysis with Infinitesimals Following Robinson, Nelson, and Others
Peter Fletcher, Karel Hrbacek, Vladimir Kanovei, Mikhail G. Katz, Claude Lobry, Sam Sanders
Real Anal. Exchange 42(2): 193-252 (2017). DOI: 10.14321/realanalexch.42.2.0193


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.


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Peter Fletcher. Karel Hrbacek. Vladimir Kanovei. Mikhail G. Katz. Claude Lobry. Sam Sanders. "Approaches to Analysis with Infinitesimals Following Robinson, Nelson, and Others." Real Anal. Exchange 42 (2) 193 - 252, 2017.


Published: 2017
First available in Project Euclid: 10 May 2018

zbMATH: 06870328
MathSciNet: MR3721800
Digital Object Identifier: 10.14321/realanalexch.42.2.0193

Primary: 03HO5 , 26E35
Secondary: 26E05

Keywords: axiomatisations , ideal elements , infinitesimal , intuitionism , multiverse , naive integers , nonstandard analysis , protozoa , set-theoretic foundations , soritical properties , superstructure , ultraproducts

Rights: Copyright © 2017 Michigan State University Press

Vol.42 • No. 2 • 2017
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