Results 11 to 20 of about 29,433 (197)
Mechanizing Nonstandard Real Analysis [PDF]
LMS Journal of Computation and Mathematics, 2000 AbstractThis paper first describes the construction and use of the hyperreals in the theorem-prover Isabelle within the framework of higher-order logic (HOL). The theory, which includes infinitesimals and infinite numbers, is based on the hyperreal number system developed by Abraham Robinson in his nonstandard analysis (NSA).
Jacques D. Fleuriot, Lawrence C. Paulson
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Forcing in nonstandard analysis
Annals of Pure and Applied Logic, 1994 The results and methods in this paper could lead to a significant improvement within the discipline of nonstandard analysis. A nonstandard universe is constructed from a superstructure in a Boolean-valued model of set theory. Much of this paper is taken up with such a construction and showing how this construction's properties compare with those of the
Ozawa, Masanao
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Realizability with Stateful Computations for Nonstandard Analysis. [PDF]
, 2021 In this paper we propose a new approach to realizability interpretations for nonstandard arithmetic. We deal with nonstandard analysis in the context of intuitionistic realizability, focusing on the Lightstone-Robinson construction of a model for nonstandard analysis through an ultrapower.
Bruno Dinis, Étienne Miquey
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On Some Types of Functions in Nonstandard Analysis
Science Journal of University of Zakho, 2016 In this paper, by using some nonstandard concepts given by Robinson and axiomatized by Nelson we study the behavior of functions defined on a discrete intervals, whose points are of infinitesimal distances.
Ibrahim O. Hamad, Sebar H. Jumha
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A constructive approach to nonstandard analysis
Annals of Pure and Applied Logic, 1995 The author introduces a constructive theory that may be useful in developing some of the areas of elementary nonstandard analysis. The theory is a conservative extension of \(\mathbf {HA}^\omega+ \mathbf {AC}\). The author adjoins a predicate, much as is done in Nelson's internal set theory, that distinguishes standard objects.
PALMGREN, E,
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NONSTANDARD COMPLETION OF NON-COMPLETE METRIC SPACE
Zanco Journal of Pure and Applied Sciences, 2021 Our aim in this study is to establishing nonstandard foundations, definitions and theorems for completion a noncomplete metric spaces. We have a lot of space or sets X which agree with all usual properties of complete, except at a small size subset
Ala O. Hassan, Ibrahim O. Hamad
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Algorithm and proof as Ω-invariance and transfer: A new model of computation in nonstandard analysis [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We propose a new model of computation based on nonstandard analysis. Intuitively, the role of "algorithm" is played by a new notion of finite procedure, called Omega-invariance and inspired by physics, from nonstandard analysis.
Sam Sanders
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Vopěnkova Alternativní teorie množin v matematickém kánonu 20. století
Filosofický časopis, 2022 Vopěnka’s Alternative Set Theory can be viewed both as an evolution and as a revolution: it is based on his previous experience with nonstandard universes, inspired by Skolem’s construction of a nonstandard model of arithmetic, and its inception has been
Haniková, Zuzana
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Mathematics, 2021 Discussions are presented by Morita and Sato in Mathematics 2017; 5, 62: 1–24, on the problem of obtaining the particular solution of an inhomogeneous ordinary differential equation with polynomial coefficients in terms of the Green’s function, in the ...
Tohru Morita, Ken-ichi Sato
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A Study on Pre-service Teachers' Discourse about Infinitesimals, Infinite Numbers, and Limits
Journal of Educational Research in Mathematics, 2021 This study investigated seven pre-service teachers’ (who studied analysis) conceptions about infinitesimals, infinite numbers, and explanation methods of limits. Some pre-service teachers thought that infinitesimals and infinite numbers existed.
Seungju Baek, Jihyun Lee
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