Approaches to analysis with infinitesimals following Robinson, Nelson, and others

Peter Fletcher, Karel Hrbáček, Vladimir Kanovei, Mikhail G. Katz, Claude Lobry, Sam Sanders

Type: Preprint

Publication Date: 2017-01-01

Citations: 16

DOI: https://doi.org/10.48550/arxiv.1703.00425

View Publication

Locations

arXiv (Cornell University) - View - PDF
Project Euclid (Cornell University) - View - PDF
DataCite API - View

Similar Works

Action	Title	Year	Authors
+ PDF Chat	Approaches To Analysis With Infinitesimals Following Robinson, Nelson, And Others	2017	Fletcher Hrbacek Kanovei Katz Lobry Sanders
+	Non-standard analysis and infinitesimals: an elementary survey	1976	B Nichols
+	Naïve Infinitesimal Analysis: Its Construction and Its Properties	2020	Anggha Satya Nugraha Maarten McKubre‐Jordens Hannes Diener
+	Na\"ive Infinitesimal Analysis: Its Construction and Its Properties.	2020	Anggha Nugraha Maarten McKubre‐Jordens Hannes Diener
+	Analyzing Benardete's comment on decimal notation	2017	Jacques Bair Piotr Błaszczyk Karin U. Katz Mikhail G. Katz Taras Kudryk David Sherry
+	Indivisibles, Infinitesimals and a Tale of Seventeenth-Century Mathematics	2013	Maureen Carroll Steven T. Dougherty David Perkins
+	Contemporary Infinitesimalist Theories of Continua and Their Late Nineteenth- and Early Twentieth-Century Forerunners	2020	Philip Ehrlich
+	Naive Foundations of Infinitesimal Analysis	2002	E. I. Gordon A. G. Kusraev S. S. Kutateladze
+	Sobre Leibniz, Newton e infinitésimos, das origens do cálculo infinitesimal aos fundamentos do cálculo diferencial paraconsistente	2006	Tadeu Fernandes de Carvalho Itala M. Lofredo D’Ottaviano
+	Elementary Axioms and Pictures for Infinitesimal Calculus	1982	David Tall
+ PDF Chat	Weyl and Intuitionistic Infinitesimals	2019	Mark van Atten
+	Andre Tacquet (S. J.) et son traite d' ≪ Arithmetique theorique et pratique ≫	1927	H. Bosmans
+	Unveiling the philosophical foundations: On Cantor’s transfinite infinites and the metaphorical accounts of infinity	2023	Osman Gazi Birgül
+	Infinitesimals	2005	Heinrich Rust
+	Mathematics of infinity	1990	Per Martin-Löf
+	The Origins of Infinitesimal Calculus	1969	MARGARET E. BARON
+	The Arithmetic of Infinitesimals	2004	John Wallis
+ PDF Chat	Ten Misconceptions from the History of Analysis and Their Debunking	2012	Piotr Błaszczyk Mikhail G. Katz David Sherry
+	Weyl and intuitionistic infinitesimals	2018	Mark van Atten
+	The Discovery of the Infinitesimal Calculus	1951	H. W. Turnbull

Works That Cite This (12)

Action	Title	Year	Authors
+ PDF Chat	Infinitesimal analysis without the Axiom of Choice	2021	Karel Hrbáček Mikhail G. Katz
+	Cauchy, infinitesimals and ghosts of departed quantifiers	2017	Jacques Bair Piotr Błaszczyk R. Ely Valérie Henry Vladimir Kanovei Kalman Katz Mikhail G. Katz Taras Kudryk S. S. Kutateladze Thomas McGaffey
+	Leibniz�s well-founded fictions and their interpetations	2018	Jacques Bair Piotr Błaszczyk R. Ely Peter Heinig Mikhail G. Katz
+	On mathematical realism and applicability of hyperreals	2019	Emanuele Bottazzi Vladimir Kanovei Mikhail G. Katz Thomas Mormann David Sherry
+ PDF Chat	Cauchy's Work on Integral Geometry, Centers of Curvature, and Other Applications of Infinitesimals	2020	Bair Błaszczyk Heinig Vladimir Kanovei Katz McGaffey
+ PDF Chat	Mathematical Conquerors, Unguru Polarity, and the Task of History	2020	Mikhail G. Katz
+ PDF Chat	Cauchy’s Infinitesimals, His Sum Theorem, and Foundational Paradigms	2017	Tiziana Bascelli Piotr Błaszczyk Alexandre Borovik Vladimir Kanovei Karin U. Katz Mikhail G. Katz S. S. Kutateladze Thomas McGaffey David Schaps David Sherry
+ PDF Chat	Historical Infinitesimalists and modern historiography of infinitesimals	2023	Mikhail G. Katz Jacques Bair Alexandre Borovik Vladimir Kanovei S. S. Kutateladze Sam Sanders David D. Sherry Monica Ugaglia
+ PDF Chat	19th-century real analysis, forward and backward	2020	Mikhail G. Katz Jacques Bair Piotr Błaszczyk Peter Heinig Vladimir Kanovei
+ PDF Chat	CONSTRUCTING NONSTANDARD HULLS AND LOEB MEASURES IN INTERNAL SET THEORIES	2022	KAREL HRBACEK Mikhail G. Katz

Works Cited by This (115)

Action	Title	Year	Authors
+	Mathematics in the alternative set theory	1979	Petr Vopěnka
+	Non-standard models in a broader perspective	2004	Haim Gaifman
+ PDF Chat	Nonstandard Asymptotic Analysis	1987	Imme van den Berg
+	Nonstandard Methods in Commutative Harmonic Analysis	1997	E. I. Gordon
+	Foundations of infinitesimal calculus	1976	H. Jerome Keisler
+ PDF Chat	The sumset phenomenon	2001	Renling Jin
+ PDF Chat	Book Review: Elementary calculus	1977	Errett Bishop
+	THEORIE RELATIVE DES ENSEMBLES INTERNES	1992	Yves Péraire
+ PDF Chat	Infinitesimals, Imaginaries, Ideals, and Fictions	2012	David Sherry Mikhail G. Katz
+	Is mathematical history written by the victors	2013	Jacques Bair Valérie Henry Piotr Błaszczyk R. Ely Vladimir Kanovei Karin U. Katz Mikhail G. Katz S. S. Kutateladze Thomas McGaffey David Schaps