Talk:Influence of non-standard analysis

From Wikipedia, the free encyclopedia
Jump to: navigation, search


As per discussion from AfD, it seems moving this to "Impact..." has a bit more support. We should also merge "Criticism..." there. Thenub314 (talk) 11:42, 19 December 2008 (UTC)

(the AfD in question being Wikipedia:Articles for deletion/Bishop–Keisler controversy for those just getting to this) —/Mendaliv//Δ's/ 17:54, 21 December 2008 (UTC)


I am placing here some notes and references that may help write a section on the influence of non-standard analysis on constructivism.

First some references I found on the web, only a few I was aware of before:

Liu, S.-C.: A proof-theoretic approach to nonstandard analysis with emphasis on distinguishing between constructive and non-constructive results, in: H.J. Keisler and K. Kunen (eds.), The Kleene Symposium, North-Holland, Amsterdam 1980, 391 - 414.

Moerdijk, I.: A model for intuitionistic non-standard arithmetic, Ann. Pure Appl. Logic 73(1995), 37 --51.

Palmgren, E.: A constructive approach to nonstandard analysis, Ann. Pure Appl. Logic 73(1995), 297 -- 325.

Palmgren, E.: Constructive nonstandard analysis, Cahiers du Centre de Logique, vol. 9, Academia, Louvain, 1996.

Palmgren, E.: Sheaf-theoretic nonstandard analysis: constructive aspects. Uppsala University, Department of Mathematics Report 1996:28.

Vesley, R.: An intuitionistic infinitesimal calculus, in: F. Richman (ed.) Constructive Mathematics, Lecture Notes in Mathematics, Vol. 873, Springer, 1983.

Wattenberg, F.: Nonstandard analysis and constructivism? Studia Logica 47(1988), 303 -- 309.

Ross, David A.: A nonstandard proof of a lemma from constructive measure theory, Mathematical Logic Quarterly, Volume 52 Issue 5, Pages 494 - 497

Also the book: "Modern Logic--A Survey: Historical, Philosophical, and Mathematical Aspects of Modern Logic and Its Applications" By Evandro Agazzi Contributor Evandro Agazzi Published by Springer, 1980 ISBN 9027711372, 9789027711373 475 pages

Has an article by J E FENSTAD titled "Logic and Probability" that contains a section about some of the applications of NSA to probability.

Here is a reference for engineering "A non-standard analysis approach to systems involving friction" by Naser Mostaghel, Journal of Sound and Vibration, Volume 284, Issues 3-5, 21 June 2005, Pages 583-595

But what we really need is a survey. Just because I can find alot of articles on say education, doesn't mean NSA has had much influence on education. Thenub314 (talk) 15:34, 19 December 2008 (UTC)

This reference seems to be a collection of research articles and survey articles, it may have some good information for this article. Sadly it is not in my library. "Nonstandard Methods And Applications in Mathematics‎" by Nigel Cutland, Mauro Di Nasso, David A. Ross - Mathematics - 2006 - 248 pages
Somehow I missed this list until now. I hope some of this material makes it into the article itself. Perhaps

if a few editors could agree to cooperate on working on this page, we could divvy up some papers that seem interesting and/or important and everyone could chip in a report. Katzmik (talk) 18:12, 21 December 2008 (UTC)