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

Autor:	Fletcher, Peter, Hrbacek, Karel, Kanovei, Vladimir, Katz, Mikhail G., Lobry, Claude, Sanders, Sam
Rok vydání:	2017
Předmět:	Mathematics - Classical Analysis and ODEs Mathematical Physics Mathematics - Differential Geometry Mathematics - History and Overview Mathematics - Logic
Zdroj:	Real Analysis Exchange 42 (2017), no. 2, 193-252
Druh dokumentu:	Working Paper
DOI:	10.14321/realanalexch.42.2.0193
Popis:	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. Comment: 54 pages, to appear in Real Analysis Exchange
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1703.00425 Zobrazit plný text záznamu View this record from Arxiv