Fletcher, P and Hrbacek, K and Kanovei, V and Katz, MG and Lobry, C and Sanders, S (2016) Approaches to analysis with infinitesimals following Robinson, Nelson, and others. Real Analysis Exchange, 42 (2). 1 -59. ISSN 0147-1937 (In Press)

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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.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Maths
Depositing User: Symplectic
Date Deposited: 07 Mar 2017 13:18
Last Modified: 07 Mar 2017 13:18
URI: http://eprints.keele.ac.uk/id/eprint/2974

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