# Tag Archives: Ultrafilters

## 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

## Convergence along ultrafilters – part II

This is the second of a series of two post whose aim is to prove the following recurrence theorem. Recall that a measure preserving system (shortened to m.p.s.) is a quadruple , where is a probability space and preserves the … Continue reading

## Convergence along ultrafilters

— 1. Introduction — On my previous post about recurrent theorems I stated Khintchine’s theorem and Sarkozy’s theorem. There I classified Khintchine’s theorem as a theorem about large intersections and Sarkozy’s theorem as a theorem about large recurrent times. This … Continue reading