Applications of nonstandard analysis to spin models

A New Approach to Nonstandard Analysis

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. To illustrate the importance of this work, we suggest comparing  a few applications of this approach with the former methods.

Finite Models of Eleimentaxy Recursive Nonstandard Analysis

This paper provides a new proof of the consistency of the formal system presented by Chuaqui and Suppes in [2, 9). First, a simpler, yet stronger, system, called Elementary Recursive Nonstandard Analysis, ERNA, will be provided. Indeed, it will be shown that ERNA proves all of the theorems of the Chuaqui and Suppes system. Then a finitary consistency proof of ERNA dl be given; in particular, we...

Finite Models of Elementary Recursive Nonstandard Analysis

This paper provides a new proof of the consistency of a formal system similar to the one presented by Chuaqui and Suppes in 2, 9]. First, a simpler, yet in some respects stronger, system, called Elementary Re-cursive Nonstandard Analysis (ERNA) will be provided. Indeed, it will be shown that ERNA proves the main axioms of the Chuaqui and Sup-pes system. Then a nitary consistency proof of ERNA w...

FOUNDATIONS OF NONSTANDARD ANALYSIS A Gentle Introduction to Nonstandard Extensions

Applications of Nonstandard Analysis in Additive Number Theory (a) = Inf

This paper reports recent progress in applying nonstandard analysis to additive number theory, especially to problems involving upper Banach density. 1 Prologue In this paper we use N for the set of all natural numbers. For any two integers a and b, a; b] denotes the interval of all integers x between a and b (a 6 x 6 b). If S is an internal set, jSj denotes the internal cardinality of S. The l...