Developments in Constructive Nonstandard Analysis

DOI10.2307/421031zbMath0920.03063OpenAlexW1997968929MaRDI QIDQ4227854

Erik Palmgren

Publication date: 31 August 1999

Published in: Bulletin of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: http://www.math.ucla.edu/~asl/bsl/0403-toc.htm

zbMATH Keywords

nonstandard hullsHeine-Borel theoreminfinitesimal analysisCauchy-Peano existence theoremBishop's constructive analysisfull transfer principleintermediate-value theoremsheaf-theorystrong idealisation principle

Mathematics Subject Classification ID

Constructive and recursive analysis (03F60) Nonstandard models in mathematics (03H05) Constructive real analysis (26E40) Nonstandard measure theory (28E05) Nonstandard analysis (26E35)

Related Items (19)

Insight in discrete geometry and computational content of a discrete model of the continuum ⋮ Saturated models of intuitionistic theories ⋮ A footnote to ``The crisis in contemporary mathematics ⋮ To be or not to be constructive, that is not the question ⋮ Foundational aspects of multiscale digitization ⋮ Nonstandard proof methods in toposes ⋮ A new approach to the \(Z\)-transform through infinite computation ⋮ Alpha-theory: An elementary axiomatics for nonstandard analysis ⋮ Weyl and Intuitionistic Infinitesimals ⋮ Ultrapowers as sheaves on a category of ultrafilters ⋮ Constructive nonstandard representations of generalized functions ⋮ Real numbers in the topos of sheaves over the category of filters ⋮ Ultrasheaves and double negation ⋮ A functional interpretation for nonstandard arithmetic ⋮ A First Look into a Formal and Constructive Approach for Discrete Geometry Using Nonstandard Analysis ⋮ Supremum, infimum and hyperlimits in the non-Archimedean ring of Colombeau generalized numbers ⋮ Reverse formalism 16 ⋮ Hyperseries in the non-Archimedean ring of Colombeau generalized numbers ⋮ REFLECTIONS ON MATHEMATICAL ECONOMICS IN THE ALGORITHMIC MODE

Cites Work

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• Eine Erweiterung der Infinitesimalrechnung
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• Nonstandard analysis and constructivism?
• A sheaf-theoretic foundation for nonstandard analysis
• Non standard analysis
• A model for intuitionistic non-standard arithmetic
• A constructive approach to nonstandard analysis
• Nonstandard analysis in practice
• What Is Nonstandard Analysis?
• Radically Elementary Probability Theory. (AM-117)

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