Results 11 to 20 of about 22,057,611 (283)
Stateful Realizers for Nonstandard Analysis [PDF]
Logical Methods in Computer Science, 2023 In this paper we propose a new approach to realizability interpretations for nonstandard arithmetic. We deal with nonstandard analysis in the context of (semi)intuitionistic realizability, focusing on the Lightstone-Robinson construction of a model for ...
Bruno Dinis, Étienne Miquey
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Grilliot's trick in Nonstandard Analysis [PDF]
Logical Methods in Computer Science, 2017 The technique known as Grilliot's trick constitutes a template for explicitly defining the Turing jump functional $(\exists^2)$ in terms of a given effectively discontinuous type two functional. In this paper, we discuss the standard extensionality trick:
Sam Sanders
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The computational content of Nonstandard Analysis [PDF]
Electronic Proceedings in Theoretical Computer Science, 2016 Kohlenbach's proof mining program deals with the extraction of effective information from typically ineffective proofs. Proof mining has its roots in Kreisel's pioneering work on the so-called unwinding of proofs.
Sam Sanders
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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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A New Approach to Nonstandard Analysis [PDF]
Sahand Communications in Mathematical Analysis, 2018 In this paper, we propose a new approach to nonstandard analysis without using the ultrafilters. This method is very simple in practice. Moreover, we construct explicitly the total order relation in the new field of the infinitesimal numbers.
Saghe Abdeljalil
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Forcing in nonstandard analysis [PDF]
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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On Some Types of Functions in Nonstandard Analysis [PDF]
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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Fuzzy Mathematics and Nonstandard Analysis Application to the Theory of Relativity [PDF]
Transactions on Fuzzy Sets and Systems, 2022 In this paper, we extend some results of nonstandard analysis to include concepts from fuzzy mathematics. Then we apply our results to issues from special and general relativity and the theory of light-clocks.
John N Mordeson, Sunil Mathew
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Categorical Nonstandard Analysis [PDF]
Symmetry, 2021 In the present paper, we propose a new axiomatic approach to nonstandard analysis and its application to the general theory of spatial structures in terms of category theory. Our framework is based on the idea of internal set theory, while we make use of an endofunctor U on a topos of sets S together with a natural transformation υ, instead of the ...
Hayato Saigo, Juzo Nohmi
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Realizability with stateful computations for nonstandard analysis [PDF]
, 2021 International audienceIn 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 ...
Miquey, Étienne, Dinis, Bruno
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