Note on Ramsey theorem for posets with linear extensions

TL;DR

This paper presents a new, concise proof of a Ramsey theorem related to partially ordered sets with multiple linear extensions, building on recent work by Solecki and Zhao.

Contribution

It offers an alternative, shorter proof of an existing theorem on Ramsey properties of posets with linear extensions.

Findings

Provided a shorter proof of the Ramsey theorem for posets with multiple linear extensions.

Confirmed the validity of the theorem through an alternative approach.

Abstract

In this note we consider a Ramsey type result for partially ordered sets. In particular, we give an alternative short proof of a theorem for a posets with multiple linear extensions recently obtained by Solecki and Zhao.