In mathematics, constructive nonstandard analysis is a version of
Abraham Robinson
Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorp ...
's
nonstandard analysis
The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal numbers. The standard way to resolve these debates is to define the operations of calculus using (ε, δ)-definitio ...
, developed by
Moerdijk
Moerdijk () is a municipality and a town in the South of the Netherlands, in the province of North Brabant.
History
The municipality of Moerdijk was founded in 1997 following the merger of the municipalities of Fijnaart en Heijningen, Klunde ...
(1995), Palmgren (1998), Ruokolainen (2004). Ruokolainen wrote:
:The possibility of
constructivization of nonstandard analysis was studied by Palmgren (1997, 1998, 2001). The model of constructive nonstandard analysis studied there is an extension of Moerdijk’s (1995) model for constructive nonstandard arithmetic.
See also
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Constructive analysis
In mathematics, constructive analysis is mathematical analysis done according to some principles of constructive mathematics.
Introduction
The name of the subject contrasts with ''classical analysis'', which in this context means analysis done acc ...
*
Smooth infinitesimal analysis
Smooth infinitesimal analysis is a modern reformulation of the calculus in terms of infinitesimals. Based on the ideas of F. W. Lawvere and employing the methods of category theory, it views all functions as being continuous and incapable of bein ...
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John Lane Bell
John Lane Bell (born March 25, 1945) is an Anglo-Canadian philosopher, mathematician and logician. He is Professor Emeritus of Philosophy at the University of Western Ontario in Canada. His research includes such topics as set theory, model theo ...
References
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Ieke Moerdijk
Izak "Ieke" Moerdijk (; born 23 January 1958) is a Dutch mathematician, currently working at Utrecht University, who in 2012 won the Spinoza Prize.
Education and career
Moerdijk studied mathematics, philosophy and general linguistics at the Uni ...
, ''A model for intuitionistic nonstandard arithmetic'', Annals of Pure and Applied Logic, vol. 73 (1995), pp. 37–51.
: "Abstract: This paper provides an explicit description of a model for intuitionistic nonstandard arithmetic, which can be formalized in a constructive metatheory without the axiom of choice
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Erik Palmgren, ''Developments in Constructive Nonstandard Analysis'',
Bulletin of Symbolic Logic Volume 4, Number 3 (1998), 233–272.
: "Abstract: We develop a constructive version of nonstandard analysis, extending
Bishop
A bishop is an ordained member of the clergy who is entrusted with a position of Episcopal polity, authority and oversight in a religious institution. In Christianity, bishops are normally responsible for the governance and administration of di ...
's
constructive analysis
In mathematics, constructive analysis is mathematical analysis done according to some principles of constructive mathematics.
Introduction
The name of the subject contrasts with ''classical analysis'', which in this context means analysis done acc ...
with infinitesimal methods. ..
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Juha Ruokolainen 2004, ''Constructive Nonstandard Analysis Without Actual Infinity
Constructivism (mathematics)
Nonstandard analysis
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