Constructive nonstandard analysis
In mathematics, constructive nonstandard analysis is a version of Abraham Robinson's nonstandard analysis, 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
- Constructive analysis
- Smooth infinitesimal analysis
- John Lane Bell
References
- Ieke Moerdijk, 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."[1]
- 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's constructive analysis with infinitesimal methods. ..."[2]
- Juha Ruokolainen 2004, Constructive Nonstandard Analysis Without Actual Infinity[3]
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Infinitesimals
- Adequality
- Leibniz's notation
- Integral symbol
- Criticism of nonstandard analysis
- The Analyst
- The Method of Mechanical Theorems
- Cavalieri's principle
- Nonstandard analysis
- Nonstandard calculus
- Internal set theory
- Synthetic differential geometry
- Smooth infinitesimal analysis
- Constructive nonstandard analysis
- Infinitesimal strain theory (physics)
- Differentials
- Hyperreal numbers
- Dual numbers
- Surreal numbers
- Analyse des Infiniment Petits
- Elementary Calculus
- Cours d'Analyse
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