On Alweiss's example for multiple recurrence

Ben Green

Abstract

In this expository note we discuss the example of R.~Alweiss giving a construction of a set $S \subset \mathbf{N}$ which intersects every nil-Bohr set, but which is not a set of $2$-recurrence.

Disclosure

“l remarks and Ryan Alweiss for correspondence about his paper. In the main part of the note, only very minor use was made of AI tools. However, I used ChatGPT 5.6 Pro to prove Proposition A.1, which shows that the set S is a set of recurrence.”
PDF page 1

Classification: Proof ideas or individual proof-step assistance
Multiplier: 8
Verified: 2026-08-23T19:09:21.517057Z

Structural counts

Pages 6 pdf

Theorems 1 source

Lemmas 1 source

Propositions 3 source

Corollaries 0 source

Definitions 1 source

Displayed equations 20 source

Bibliography entries 8 source

Appendix pages 2 estimated

Count notes

Source counts use the expanded primary TeX file main.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.