A List of Problems on the Reverse Mathematics of Ramsey Theory on the Rado Graph and on Infinite, Finitely Branching Trees

TL;DR

This paper compiles open problems in the Reverse Mathematics of infinitary Ramsey theory related to the Rado graph and infinite, finitely branching trees, aiming to motivate further research in the field.

Contribution

It provides a curated list of unresolved problems in the Reverse Mathematics of Ramsey theory on specific infinite structures, encouraging collaborative problem-solving.

Findings

Identifies key open problems in the field

Provides background and references for further study

Aims to stimulate research and collaboration

Abstract

This list presents problems in the Reverse Mathematics of infinitary Ramsey theory which I find interesting but do not personally have the techniques to solve. The intent is to enlist the help of those working in Reverse Mathematics to take on such problems, and the myriad of related questions one can infer from them. A short bit of background and starting references are provided.