# Tag Archives: Szemeredi’s theorem

## Szemerédi Theorem Part VI – Dichotomy between weak mixing and compact extension

This is the sixth and final post in a series about Szemerédi’s theorem. In this post I complete the proof of the Multiple Recurrence Theorem, which I showed in a previous post of this series to be equivalent to Szemerédi’s … Continue reading

## Szemerédi’s Theorem Part V – Compact extensions

This is the fifth in a series of six posts I am writing about Szemerédi’s theorem. In the previous post I proved that the Sz property lifts through weak mixing extension and in this post I will prove that the … Continue reading

## Szemerédi’s Theorem Part IV – Weak mixing extensions

This is the fourth in a series of six posts I am writing about Szemerédi’s theorem. In the first three posts, besides setting up the notation and definitions necessary, I reduced Szemerédi’s theorem to three facts. Those three facts are … Continue reading

Posted in Ergodic Theory | | 2 Comments

## Pomerance Theorem on colinear points in certain paths in a two dimensional lattice

— 1. Introduction — Van der Waerden’s theorem (to which I gave two proofs in previous posts on this blog) states that if one colors the positive integers with finitely many colors, then one can always find a monochromatic arithmetic … Continue reading

Posted in Combinatorics, Ramsey Theory | Tagged , | 1 Comment

## Szemerédi’s Theorem Part III – Precise definitions

This is the third in a series of six posts on Szemerédi’s theorem. In the previous post I outlined the ideas of the ergodic theoretical proof by Furstenberg. In this post I will set up the machinery and give the … Continue reading

Posted in Combinatorics, Ergodic Theory, Ramsey Theory | | 3 Comments

## Szemerédi’s Theorem Part II – Overview of the proof

This is the second in a series of posts about Szemerédi’s theorem. In the first post I presented the first step in the proof of Szemerédi’ theorem, namely applying the correspondence principle of Furstenberg to transform the problem into one … Continue reading

Posted in Combinatorics, Ergodic Theory | | 4 Comments

## Szemerédi’s Theorem Part I – Equivalent formulations

The theorem of van der Waerden on arithmetic progressions, whose precise statement and proof can be found in a previous post of mine, states that in a finite partition of the set of positive integers, one of the pieces contains … Continue reading

Posted in Combinatorics, Ergodic Theory, Ramsey Theory | | 6 Comments