Approaches To Analysis With Infinitesimals Following Robinson, Nelson, And Others

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 theIntended Interpretationhypothesis. We highlight some applic...

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Bibliographic Details
Published inReal analysis exchange Vol. 42; no. 2; pp. 193 - 252
Main Authors Fletcher, Peter, Hrbacek, Karel, Kanovei, Vladimir, Katz, Mikhail G., Lobry, Claude, Sanders, Sam
Format Journal Article
LanguageEnglish
Published East Lansing Michigan State University Press 01.01.2017
Subjects
Animals
Axioms
Differential geometry
Equivalence relation
Geometry
Mathematical set theory
Mathematical sets
Mathematics
Nonstandard analysis
Numbers
Real numbers
Superstructures
Topical Survey
Ultrapowers
Zermelo Frankel set theory
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Summary: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 theIntended Interpretationhypothesis. 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. Mathematical Reviews subject classification: Primary: 03HO5, 26E35; Secondary: 26E05 Key words: axiomatisations, infinitesimal, nonstandard analysis, ultraproducts, super-structure, set-theoretic foundations, multiverse, naive integers, intuitionism, soritical properties, ideal elements, protozoa
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0147-1937
1930-1219
DOI:10.14321/realanalexch.42.2.0193