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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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.

Article information

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

Dates
First available in Project Euclid: 10 May 2018

Permanent link to this document
https://projecteuclid.org/euclid.rae/1525917686

Digital Object Identifier
doi:10.14321/realanalexch.42.2.0193

Mathematical Reviews number (MathSciNet)
MR3721800

Zentralblatt MATH identifier
06870328

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

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

Citation

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. https://projecteuclid.org/euclid.rae/1525917686


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