Partitioning $\alpha$-large sets for $\alpha<\varepsilon_{\omega}$

TL;DR

This paper extends the partitioning of alpha-large sets to a broader class of ordinals below epsilon_omega, providing tools for miniaturizing the infinite Ramsey Theorem.

Contribution

It generalizes previous results on partitioning alpha-large sets to include all ordinals below epsilon_omega, expanding their applicability.

Findings

Extended partitioning results to ordinals below epsilon_omega.

Facilitated miniaturization of the infinite Ramsey Theorem.

Provided a framework for future combinatorial applications.

Abstract

We generalise the results by Bigorajska and Kotlarski about partitioning $\alpha$-large sets, by extending the domain up to ordinals below $\varepsilon_{\omega}$. These results will be very useful to give a miniaturisation of the infinite Ramsey Theorem.