Rothberger's property in finite powers

TL;DR

This paper establishes that classical Ramseyan principles and certain forcing statements are equivalent to a topological property called Rothberger's property across all finite powers, linking combinatorial and topological concepts.

Contribution

It proves the equivalence between classical Ramseyan statements, forcing statements, and Rothberger's property in all finite powers, unifying these concepts.

Findings

Classical Ramseyan statements are equivalent to Rothberger's property in finite powers.

Forcing statements are also equivalent to Rothberger's property in finite powers.

The results connect combinatorial, topological, and set-theoretic principles.

Abstract

We show that several classical Ramseyan statements, and a forcing statement, are each equivalent to having Rothberger's property in all finite powers.