# Tag Archives: Stone-Cech compactification

## A proof of the Erdős sumset conjecture

Florian Richter, Donald Robertson and I have uploaded to the arXiv our paper entitled A proof of the Erdős sumset conjecture. The main goal of the paper is to prove the following theorem, which verifies a conjecture of Erdős discussed … Continue reading

## 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 Poincaré 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