# Ramsey's coheirs

## TL;DR

This paper employs model theoretic coheir concepts to provide concise proofs of classical and modern theorems in Ramsey Theory, including Ramsey's, Hindman's, and Hales-Jewett theorems, as well as principles leading to Carlson and Gowers partition theorems.

## Contribution

It introduces a novel model theoretic approach using coheirs to simplify and unify proofs of key results in Ramsey Theory.

## Key findings

- Short proofs of Ramsey's, Hindman's, and Hales-Jewett theorems
- New Ramsey theoretic principles related to Carlson and Gowers
- Unified model theoretic framework for classical Ramsey results

## Abstract

We use the model theoretic notion of coheir to give short proofs of old and new theorems in Ramsey Theory. As an illustration we start from Ramsey's theorem itself. Then we prove Hindman's theorem and the Hales-Jewett theorem. Finally, we prove two Ramsey theoretic principles that have among their consequences partition theorems of Carlson and of Gowers.