Keele Research Repository
Explore the Repository
Fletcher, P, Hrbacek, K, Kanovei, V, Katz, MG, Lobry, C and Sanders, S (2017) Approaches to analysis with infinitesimals following Robinson, Nelson, and others. Real Analysis Exchange, 42 (2). 1 -59. ISSN 0147-1937
approaches.pdf - Accepted Version
Available under License Creative Commons Attribution Non-commercial.
Download (564kB) | Preview
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 Mathematics |
Depositing User: | Symplectic |
Date Deposited: | 07 Mar 2017 13:18 |
Last Modified: | 20 Nov 2017 15:27 |
URI: | https://eprints.keele.ac.uk/id/eprint/2974 |