# The closed ordinal Ramsey number $R^{cl}(\omega^2,3) = \omega^6$

## TL;DR

This paper determines the exact value of a topological variant of the ordinal Ramsey number for specific ordinals, advancing understanding in ordinal combinatorics.

## Contribution

It provides the first precise calculation of the closed ordinal Ramsey number for , , a significant step in ordinal Ramsey theory.

## Key findings

- Exact value of R^{cl}(\u03c9^2,3) = 
- Advances the understanding of topological ordinal Ramsey numbers
- Establishes a new benchmark for future ordinal Ramsey calculations

## Abstract

Closed ordinal Ramsey numbers are a topological variant of the classical (ordinal) Ramsey numbers. We compute the exact value of the closed ordinal Ramsey number $R^{cl}(\omega^2,3) = \omega^6$.