A Ramsey theorem for partial orders with linear extensions

TL;DR

This paper establishes a new Ramsey theorem for finite sets with partial orders and multiple linear extensions, generalizing previous results and providing new proof techniques.

Contribution

It introduces a generalized Ramsey theorem for partial orders with linear extensions, unifying and extending recent related theorems.

Findings

Proves a Ramsey theorem for finite partial orders with linear extensions

Provides new proof techniques applicable to existing theorems

Unifies two recent Ramsey theorems into a broader framework

Abstract

We prove a Ramsey theorem for finite sets equipped with a partial order and a fixed number of linear orders extending the partial order. This is a common generalization of two recent Ramsey theorems due to Soki\'c. As a bonus, our proof gives new arguments for these two results.