Related papers: Nonstandard Analysis: Its Creator and Place
These lecture notes, to be completed in a later version, offer a short and rigorous introduction to Nostandard Analysis, mainly aimed to reach to a presentation of the basics of Loeb integration, and in particular, Loeb measures. The…
We characterize Schwartz distributions having a value at a single point in the sense introduced by means of nonstandard analysis by A. Robinson. They appear to be distributions continuous in a neighborhood of the point.
This is a survey of several approaches to the framework for working with infinitesimals and infinite numbers, originally developed by Abraham Robinson in the 1960s, and their constructive engagement with the Cantor-Dedekind postulate and…
In this article we use our constructions from "Enlargements of Categories" (Theory and Applications of Categories, 14:357-398) to lay down some foundations for the application of A. Robinson's nonstandard methods to modern Algebraic…
There have been extensive developments recently in modern nonparametric inference and modeling. Nonparametric and semi-parametric methods are especially useful with large amounts of data that are now routinely collected in many areas of…
The goal of this present manuscript is to introduce the reader to the nonstandard method and to provide an overview of its most prominent applications in Ramsey theory and combinatorial number theory.
Abraham Robinson's framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Their procedures have been often viewed through the lens of the…
A short tutorial on non-standard analysis, made in particular for people working in the Categorical Quantum Mechanics crowd.
Nonlinear science has evolved significantly over the 35 years since the launch of the journal Chaos. This Focus Issue, dedicated to the 80th Birthday of its founding editor-in-chief, David K. Campbell, brings together a selection of…
This is a Research and Instructional Development Project from the U. S. Naval Academy. In this monograph, the basic methods of nonstandard analysis for n-dimensional Euclidean spaces are presented. Specific rules are deveoped and these…
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…
Reverse Mathematics (RM) is a program in the foundations of mathematics founded by Friedman and developed extensively by Simpson. The aim of RM is finding the minimal axioms needed to prove a theorem of ordinary (i.e. non-set theoretical)…
This is a short overview of the influence of mathematicians and their ideas on the creative contribution of Mikhailo Lomonosov on the occasion of the tercentenary of his birth.
This paper, which is dedicated to Alan Turing on the 50th anniversary of his death, gives an overview and discusses the philosophical implications of incompleteness, uncomputability and randomness.
In this monograph, nonstandard characteristics for many notions from real analysis are obtained and applied. However, only two simple types of atomic formula are used and almost all of the characteristics are shown to hold for a simple…
Almost two decades ago, Wattenberg published a paper with the title 'Nonstandard Analysis and Constructivism?' in which he speculates on a possible connection between Nonstandard Analysis and constructive mathematics. We study Wattenberg's…
This note has two principal aims: to portray an essence of Non-Standard Analysis as a particular structure (which we call lim-rim), noting its interplay with the notion of ultrapower, and to present a construction of Non-Standard Analysis,…
By presenting the proofs of a few sample results, we introduce the reader to the use of nonstandard analysis in aspects of combinatorics of numbers.
Currently the two popular ways to practice Robinson's nonstandard analysis are the model-theoretic approach and the axiomatic/syntactic approach. It is sometimes claimed that the internal axiomatic approach is unable to handle constructions…
We apply methods of nonstandard mathematics in order to regard analytic geometry in a very different way. For example, complex spaces are seen to be the "standard part" of certain algebraic nonstandard schemes. We construct a category of…