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

Peter Fletcher, Karel Hrbacek, Vladimir Kanovei, Mikhail G. Katz, Claude Lobry, Sam Sanders

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


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.

Original languageEnglish
Pages (from-to)193-252
Number of pages60
JournalReal Analysis Exchange
Issue number2
StatePublished - 2017

Bibliographical note

Funding Information:
We are grateful to Eric Leichtnam and Dalibor Praˇzák for helpful comments on an earlier version of the manuscript. Vladimir Kanovei was supported in part by the RFBR grant number 17-01-00705. M. Katz was partially supported by Israel Science Foundation grant no. 1517/12. S. Sanders was supported by the following funding bodies: FWO Flanders, the John Templeton Foundation, the Alexander von Humboldt Foundation, and the Japan Society for the Promotion of Science, and expresses gratitude towards these institutions.


  • Axiomatisations
  • Ideal elements
  • Infinitesimal
  • Intuitionism
  • Multiverse
  • Naive integers
  • Nonstandard analysis
  • Protozoa
  • Set-theoretic foundations
  • Soritical properties
  • Superstructure
  • Ultraproducts


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