
Recent Posts
 An arithmetic van der Corput trick and the polynomial van der Waerden theorem
 Piecewise syndetic sets, topological dynamics and ultrafilters
 Measure preserving actions of affine semigroups and {x+y,xy} patterns
 SzemerĂ©di Theorem Part VI – Dichotomy between weak mixing and compact extension
 Gaussian systems
Tag Archives: StoneCech compactification
Measure preserving actions of affine semigroups and {x+y,xy} patterns
Vitaly Bergelson and I have recently submitted to the arXiv our paper entitled `Measure preserving actions of affine semigroups and patterns’. The main purpose of this paper is to extend the results of our previous paper, establishing some partial progress … Continue reading
Jin’s Theorem
— 1. Introduction — The PoincarĂ© recurrence theorem (or, more accurately, its proof) implies that, given a set with positive upper Banach density, i.e. then there exists some such that . In fact one gets that the set of those … Continue reading
Properties of ultrafilters and a Theorem on arithmetic combinatorics
A Theorem of Schur (one of the earliest results in Ramsey Theory) asserts that given any finite coloring of the set of natural numbers , there exist of the same color such that also has the same color. As a … Continue reading
Posted in Combinatorics, Ramsey Theory
Tagged Hindman, ramsey theory, rings, StoneCech compactification, Ultrafilters
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