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 (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
*
Smooth infinitesimal analysis
*
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 theor ...
References
*
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 Un ...
, ''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
*
Erik Palmgren, ''Developments in Constructive Nonstandard Analysis'',
Bulletin of Symbolic Logic
Bulletin or The Bulletin may refer to:
Periodicals (newspapers, magazines, journals)
* Bulletin (online newspaper), a Swedish online newspaper
* ''The Bulletin'' (Australian periodical), an Australian magazine (1880–2008)
** Bulletin Debate ...
Volume 4, Number 3 (1998), 233–272.
: "Abstract: We develop a constructive version of nonstandard analysis, extending
Bishop
A bishop is an ordained clergy member who is entrusted with a position of authority and oversight in a religious institution.
In Christianity, bishops are normally responsible for the governance of dioceses. The role or office of bishop is ...
's constructive analysis with infinitesimal methods. ..
*
Juha Ruokolainen
Juha is a masculine given name of Finnish origin derived from Johannes (or John in English language contexts). Notable people with the name include:
* Juha Alén
* Juha Gustafsson
* Juha Hakola
* Juha Harju
* Juha Haukkala
* Juha Hautamäk ...
2004, ''Constructive Nonstandard Analysis Without Actual Infinity
Constructivism (mathematics)
Nonstandard analysis
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