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Page 5649 of Mathematical Reviews Vol. , Issue 88k [page]

1988 Mathematical Reviews  
The axioms of *NST say that the universe satisfies the axioms of ZFC minus foundation, the set J of internal sets is transitive, foundation holds for sets disjoint from J, there is an elementary embedding  ...  This is a paper written with the aim of convincing people working in mathematical and theoretical physics that nonstandard analysis can be of considerable use for them, and the amount of new mathematical  ... 

Book Review: Foundations of infinitesimal stochastic analysis

D. N. Hoover
1989 Bulletin of the American Mathematical Society  
The set theoretic foundation has indeed made mathematics into a well-defined deductive science, but it has made it less accessible to the nonspecialists who should be actually applying it, has encumbered  ...  For example, applied probabilists commonly regard the measure theoretic foundations of their discipline as something to be avoided and ignored as far as possible, which is pretty far.  ... 
doi:10.1090/s0273-0979-1989-15832-1 fatcat:3xc6f7tuqzgitnkcf3yi33jszy

Nonstandard analysis: Its creator and place

S. S. Kutateladze
2013 Journal of Applied and Industrial Mathematics  
This is a biographical sketch and tribute to Abraham Robinson (1918-1974) on the 95th anniversary of his birth with a short discussion of the place of nonstandard analysis in the present-day mathematics  ...  The above demonstrates that the nonstandard methods of analysis, i. e., the techniques based on simultaneous consideration of standard and nonstandard set-theoretic models, is not something especial, indecent  ...  Therefore, the common method of depicting numbers by points is an example of nonstandard set theoretic modeling. 6 Cp. [12] .  ... 
doi:10.1134/s1990478913030010 fatcat:it3v7eh3uffapjo3gsuppepn2i

Book Review: Radically elementary probability theory

Loren D. Pitt
1989 Bulletin of the American Mathematical Society  
As a replacement for the conventional measure theoretic foundations of probability, Nelson proposes elementary finite probability spaces and a "tiny bit of nonstandard analysis."  ...  Nonstandard analysis was created by Abraham Robinson in 1960 to lay a rigorous foundation for infinitesimals in analysis.  ... 
doi:10.1090/s0273-0979-1989-15779-0 fatcat:hsvp7uj42ng5pelhjo5qqbb5du

Page 3416 of Mathematical Reviews Vol. , Issue 97F [page]

1997 Mathematical Reviews  
of nonstandard analysis over various set universes for each infinite «, might not provide a less satisfactory and attractive “theoretical system of foundations” for nonstandard mathematics [see D.  ...  We conclude with some comments on the possible role the pre- sented theories could play as foundations for nonstandard analysis.  ... 

Page 7315 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
The class of standard ele- ments is a model of ZFC; *ZFC and ZFC are equiconsistent.” 97m:03098 03HO0S 03F60 Paimgren, Erik (S-UPPS; Uppsala) A sheaf-theoretic foundation for nonstandard analysis.  ...  Summary: “A new foundation for constructive nonstandard anal- ysis is presented. It is based on an extension of a sheaf-theoretic model of nonstandard arithmetic due to I. Moerdijk.  ... 

Page 5332 of Mathematical Reviews Vol. , Issue 97I [page]

1997 Mathematical Reviews  
Then @ is called a nonstandard embedding. The non- standard model # and the nonstandard embedding @ are called strong if the condition (*) holds for every set-theoretic formula y.  ...  A nonstandard a-model @ is a pair # = (M, €.4) together with a mapping 0: V,(X) — M satisfying (*) (Va(X),€) = plai,-++,dn) <> M & v(0(a)),---,0(a,)) for any a\,---,a, € Va(X) and every bounded set-theoretic  ... 

Page 2542 of Mathematical Reviews Vol. , Issue 84g [page]

1984 Mathematical Reviews  
The definitions are given in the terminology of nonstandard analysis. Chapter 4 is devoted to a general nonstandard axiomatization of set theory. The axiom system consists of E.  ...  Robinson gave an exact foundation of the calculus of infinitesimals and showed that nonstandard analysis is a general method with applications in many mathematical theories.  ... 

Page 6419 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
Then two disadvantages of the model-theoretic version of nonstandard analysis are men- tioned: the need to use different nonstandard models for different problems, and the cumbersome apparatus of the higher-order  ...  Since this paper was written, another nonstandard set theory, called EST (enlargement set the- ory), has been proposed by D. Ballard [Foundational aspects of “non” standard mathematics, Contemp.  ... 

Book Review: Nonstandard methods in stochastic analysis and mathematical physics

A. E. Hurd
1987 Bulletin of the American Mathematical Society  
A large part of the book under review is devoted to applications of nonstandard analysis to various aspects of probability theory, and the foundations are presented in Chapter three.  ...  This led to the great variety of applications that we see today. Robinson's book Nonstandard analysis [15] appeared in 1966 and set the stage  ... 
doi:10.1090/s0273-0979-1987-15607-2 fatcat:f77lhpng4jd5thzptdttwbx3da

Page 4420 of Mathematical Reviews Vol. , Issue 86j [page]

1986 Mathematical Reviews  
Whether or not such an analysis of a proof written within the language of nonstandard analysis for a standard theorem shows that the proof is “simpler” and that the proof concepts have special relevance  ...  Andréka et al., Theoret. Comput.  ... 

Page 1359 of Mathematical Reviews Vol. , Issue 83d [page]

1983 Mathematical Reviews  
The author gives an expository account of nonstandard analysis, sketching the ultrapower construction of nonstandard models and describing simple applications of nonstandard analysis in calculus and topology  ...  Those who try to avoid formal languages and are working in category theory or universal algebra will find in this article a foundation for nonstandard analysis without formal logic.  ... 

Page 1833 of Mathematical Reviews Vol. , Issue 86e [page]

1986 Mathematical Reviews  
The permanence principle of nonstandard analysis states that an internal property that holds on the set of all standard elements in the extension of an infinite standard set must continue to hold on some  ...  Mittelstaedt, Peter (D-KOLN-P) 86e:03059 Analysis of the EPR-experiment by relativistic quantum logic. Foundations of quantum mechanics in the light of new technology ( Tokyo, 1983), 251-255, Phys.  ... 

Page 3440 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
It is also a critique of (radical) formalism in mathematics. The author discusses the foundations of calculus (the basic axioms) and of nonstandard analysis (Internal Set Theory [E. Nelson, Bull.  ...  Later in the chapter, a new axiomatization of nonstandard analysis, the so-called nonstan- dard class theory (a conservative extension of Nelson’s Internal Set Theory, encompassing the nonstandard hull  ... 

The Trend of Logic and Foundation of Mathematics in Japan in 1991 to 1996

Yuzuru KAKUDA, Kanji NAMBA, Nobuyoshi MOTOHASHI
1997 Annals of the Japan Association for Philosophy of Science  
A nonstandard approach to diffusions on manifolds and nonstandard heat kernels, in "Analysis, Probability and Mathematical Physics : Contribu- tions of Nonstandard Analysis" (S. Albeverio, W.A.J.  ...  Ozawa developed forcing in nonstandard analysis and tried to apply to functional analysis.  ... 
doi:10.4288/jafpos1956.9.95 fatcat:g3ppep2v5jam3n7n5stre7ljdu
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