THE ULTRAPRODUCT CONSTRUCTION 1. Introduction The ultraproduct construction is a
uniform method of building models of first orde Page 1 THE ULTRAPRODUCT CONSTRUCTION …

The eightfold path to nonstandard analysis Page 15 THE EIGHTFOLD PATH TO
NONSTANDARD ANALYSIS VIERI BENCI, MARCO FORTI, AND MAURO DI NASSO Abstract …

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By using nonstandard analysis, and in particular iterated hyper-extensions, we give
foundations to a peculiar way of manipulating ultrafilters on the natural numbers and their …

In literature, many important combinatorial properties of subsets of N have been studied both
with nonstandard techniques and from the point of view of N. In this thesis we mix these two …

We give the name Hausdorff to those ultrafilters that provide ultrapowers whose natural
topology ($ S $-topology) is Hausdorff, eg selective ultrafilters are Hausdorff. Here we give …

We introduce a notion of topological extension of a given set X. The resulting class of
topological spaces includes the Stone-Čech compactification β X of the discrete space X, as …

An extension of the divisibility relation on $\mathbb {N} $ to the set $\beta\mathbb {N} $ of
ultrafilters on $\mathbb {N} $ was defined and investigated in several papers during the last …

We use nonstandard methods, based on iterated hyperextensions, to develop applications
to Ramsey theory of the theory of monads of ultrafilters. This is performed by studying in …

Nonstandard analysis is often presented as a part of logic. This habit is, in our opinion, a
mere historical accident. In fact, several different approches are possible. Eg, it is shown in …