Real Analysis Exchange

Approaches to Analysis with Infinitesimals Following Robinson, Nelson, and Others

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

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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.

Article information

Real Anal. Exchange, Volume 42, Number 2 (2017), 193-252.

First available in Project Euclid: 10 May 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03HO5 26E35: Nonstandard analysis [See also 03H05, 28E05, 54J05]
Secondary: 26E05: Real-analytic functions [See also 32B05, 32C05]

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


Fletcher, Peter; Hrbacek, Karel; Kanovei, Vladimir; Katz, Mikhail G.; Lobry, Claude; Sanders, Sam. Approaches to Analysis with Infinitesimals Following Robinson, Nelson, and Others. Real Anal. Exchange 42 (2017), no. 2, 193--252. doi:10.14321/realanalexch.42.2.0193.

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