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arXiv · 1703.00425

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

Peter Fletcher·Karel Hrbacek·Vladimir Kanovei·Mikhail G. Katz·Claude Lobry·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. Keywords: axiomatisations, infinitesimal, nonstandard analysis, ultraproducts, superstructure, set-theoretic foundations, multiverse, naive integers, intuitionism, soritical properties, ideal elements, protozoa.

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Peter Fletcher, Karel Hrbacek, Vladimir Kanovei, Mikhail G. Katz, Claude Lobry, Sam Sanders. 2017-03-01. Approaches to analysis with infinitesimals following Robinson, Nelson, and others. https://doi.org/10.14321/realanalexch.42.2.0193

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