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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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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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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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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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On Infinitesimal L_ω-smooth Functions.
Zanco Journal of Pure and Applied Sciences, 2022 The aim of this paper is to study smoothness, approximate continuity, and approximate derivative in a nonstandard manner with respect to infinitesimal parameters.
Ibrahim O. Hamad
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Міжнародний науково-технічний журнал "Проблеми керування та інформатики", 2022 Various technical and other realworld systems can be modelled with decent precision as linear systems. This approach is the core of the long established control theory, whose mathematical apparatus is ubiquitous when it comes to controlling some kind of
Михайло Дмитрович Міщенко
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Improved Definition of NonStandard Neutrosophic Logic and Introduction to Neutrosophic Hyperreals (Fifth version) [PDF]
Neutrosophic Sets and Systems, 2022 In the fifth version of our response-paper [26] to Imamura’s criticism, we recall that NonStandard Neutrosophic Logic was never used by neutrosophic community in no application, that the quarter of century old neutrosophic operators (1995-1998 ...
Florentin Smarandache
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Nonstandard analysis in topology: nonstandard and standard compactifications [PDF]
Journal of Symbolic Logic, 2000 AbstractLet (X, T) be a topological space and *X a nonstandard extension of X. Sets of the form *G. where G ∈ T, form a base for the “standard” topology ST on *X. The topological space (*X, ST) will be used to study compactifications of (X, T) in a systematic way.
Salbany, S., Todorov, Todor D.
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