Talk:Influence of non-standard analysis
- (the AfD in question being Wikipedia:Articles for deletion/Bishop–Keisler controversy for those just getting to this) —/Mendaliv/2¢/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
- 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)