The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.

## Filters

##
###
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

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. ...

##
###
Nonstandard analysis: Its creator and place

2013
*
Journal of Applied and Industrial Mathematics
*

This is a biographical sketch and tribute to Abraham Robinson (1918-1974) on

doi:10.1134/s1990478913030010
fatcat:it3v7eh3uffapjo3gsuppepn2i
*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] . ...##
###
Book Review: Radically elementary probability theory

1989
*
Bulletin of the American Mathematical Society
*

As a replacement for

doi:10.1090/s0273-0979-1989-15779-0
fatcat:hsvp7uj42ng5pelhjo5qqbb5du
*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*. ...##
###
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

1987
*
Bulletin of the American Mathematical Society
*

A large part

doi:10.1090/s0273-0979-1987-15607-2
fatcat:f77lhpng4jd5thzptdttwbx3da
*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 ...##
###
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

1997
*
Annals of the Japan Association for Philosophy of Science
*

A

doi:10.4288/jafpos1956.9.95
fatcat:g3ppep2v5jam3n7n5stre7ljdu
*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*. ...
« Previous

*Showing results 1 — 15 out of 9,670 results*