EDWARD NELSON (1932–2014)

@article{Katz2015EDWARDN,
  title={EDWARD NELSON (1932–2014)},
  author={M. Katz and S. Kutateladze},
  journal={The Review of Symbolic Logic},
  year={2015},
  volume={8},
  pages={607 - 610}
}
In the article we give an appreciation of Edward Nelson's multifaceted contribution to mathematics, and particularly to foundational theories of infinitesimals. 

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References

SHOWING 1-10 OF 17 REFERENCES
Radically Elementary Probability Theory
The expressive power of minIST comes from the fact that it allows for the notions of finite sets with unlimited cardinality, and finite subsets of the reals whose distance is at most an infinitesimalExpand
Comments on Edward Nelson’s “Internal set theory: A new approach to nonstandard analysis”
Do infinitesimals exist? This question arises naturally in calculus when one wants to write f(x+Δx) f(x) + f ′(x)Δx. This equation should hold for infinitesimal Δx where the notation a b means thatExpand
Is mathematical history written by the victors
The ABCs of the History of Infinitesimal Mathematics The ABCs of the history of infinitesimal mathematics are in need of clarification. To what extent does the famous dictum “history is alwaysExpand
Leibniz versus Ishiguro: Closing a Quarter Century of Syncategoremania
Did Leibniz exploit infinitesimals and infinities à la rigueur or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Hidé Ishiguro defends the latterExpand
Nonstandard Analysis, Axiomatically
1 Getting started.- 2 Elementary real analysis in the nonstandard universe.- 3 Theories of internal sets.- 4 Metamathematics of internal theories.- 5 Definable external sets and metamathematics ofExpand
The International Society for the History of Philosophy of Science
The present issue brings us one small step closer to the resumption of a more timely publication schedule, and just in time for upcoming HOPOS 2006 in Paris! The complete program for this meetingExpand
Non-Standard Analysis
1. As early as 1934 it was pointed out by Thoralf Skolem (see [17]) that there exist proper extensions of the natural number system which have, in some sense, ‘the same properties’ as the naturalExpand
The syntax of nonstandard analysis
  • E. Nelson
  • Mathematics, Computer Science
  • Ann. Pure Appl. Log.
  • 1988
Etude de la syntaxe de l'analyse non standard et resolution d'un probleme pose par A. Robinson concernant les nouvelles procedures deductives
Diffusion, quantum theory, and radically elementary mathematics
Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is alsoExpand
Internal set theory: A new approach to nonstandard analysis
1. Internal set theory. We present here a new approach to Abraham Robinson's nonstandard analysis [10] with the aim of making these powerful methods readily available to the working mathematician.Expand
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