Related papers: Hypernatural Numbers as Ultrafilters
A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper…
This is a translation into English of a paper written in French, published in Tatra Mountains Mathematical Publications, {L'ultrafiltre, un outil incomparable}, Tatra Mt. Math. Publ. {\bf 31} (2005), 131-176.It was also posted as…
We investigate the structure of ultrafilters on Boolean algebras in the framework of Tukey reducibility. In particular, this paper provides several techniques to construct ultrafilters which are not Tukey maximal. Furthermore, we connect…
In recent years, several problems regarding the partition regularity of exponential configurations have been studied in the literature, in some cases using the properties of specific ultrafilters. In this paper, we start to lay down the…
We consider the bounds imposed by naturalness on the masses of superpartners for arbitrary points in nonminimal supersymmetric extensions of the standard model and for arbitrary messenger scales. This constitutes a significant…
A discussion of several exotic models and how well they are able to describe the data, with particular emphasis on atmospheric neutrinos.
We develop the theory of cofinal types of ultrafilters over measurable cardinals and establish its connections to Galvin's property. We generalize fundamental results from the countable to the uncountable, but often in surprisingly…
This application of nonstandard analysis utilizes the notion of the highly-staturated enlargement. These nonstandard methods clarify many aspects of the theory of generalized functions (distributions).
We present some new results on union ultrafilters. We characterize stability for union ultrafilters and, as the main result, we construct a new kind of unordered union ultrafilter.
We show some non-standard Poincar\'e type estimates in the biparametric setting with appropriate weights. We will derive these results using variants from classical estimates exploiting the interplay between maximal functions and fractional…
We extend theories of reverse mathematics by a non-principal ultrafilter, and show that these are conservative extensions of the usual theories ACA0, ATR0, and Pi11-Comprehension.
Given an ordered structure, we study a natural way to extend the order to preorders on type spaces. For definably complete, linearly ordered structures, we give a characterisation of the preorder on the space of 1-types. We apply these…
Nonstandard graphs have been defined and examined in prior works. The present work does the same for nonstandard digraphs. Since digraphs have more structure than do graphs, the present discussion requires more complicated definitions and…
It was recently shown that arbitrary first-order models canonically extend to models (of the same language) consisting of ultrafilters. The main precursor of this construction was the extension of semigroups to semigroups of ultrafilters, a…
Highly saturated models are a fundamental part of the model-theoretic machinery of nonstandard analysis. Of the two methods for producing them, ultrapowers constructed with the aid of $\kappa^+$-good ultrafilters seems by far the less…
We discuss an extension of classical combinatorics theory to the case of spatially distributed objects.
We show that many important natural science models in their mathematical formulation can be reduced to non-strictly hyperbolic systems of the same kind. This allows the same methods to be applied to them so that some essential results…
In this paper, we study a special type of ultrafilter which we call Shelah ultrafilter. We show that it is possible to add a Shelah ultrafilter using a special forcing notion. We also show that Shelah ultrafilters turn out to be…
A set of natural numbers will be called \emph{harmonic} if the reciprocals of its elements form a divergent series. An ultrafilter of the natural numbers will he called \emph{harmonic} if all each members are harmonic sets. The harmonic…
We survey recent developments on rationality problems for algebraic varieties, with a particular emphasis on cycle-theoretic and combinatorial methods and their applications to hypersurfaces.