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

Abstract

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

22 pages