A Note on "Regularity lemma for distal structures"

TL;DR

This paper provides a concise, purely model-theoretic proof that graphs in distal theories exhibit strong regularity properties, extending previous semi-algebraic results.

Contribution

It offers a shorter, model-theoretic proof of regularity in distal graphs, simplifying and generalizing prior semi-algebraic approaches.

Findings

Graphs in distal theories have strong regularity properties

The proof is shorter and purely model-theoretic

Extends previous semi-algebraic results

Abstract

In a recent paper, Chernikov and Starchenko prove that graphs defined in distal theories have strong regularity properties, generalizing previous results about graphs defined by semi-algebraic relations. We give a shorter, purely model-theoretic proof of this fact.