## Van der Waerden’s Theorem is false for $latex \omega_1$

One of my main research problems involves something I think is related to arithmetic progressions in $\mathbb{Z}$. After learning a nice proof of Van der Waerden’s Theorem, and sharing it with colleagues, Daniel Soukup asked a nice question about Van der Waerden’s Theorem on $\omega_1$. We answered it, and the example was sufficiently nice that I would like to share it.

## Van der Waerden’s Theorem is false for $latex omega_1$

One of my main research problems involves something I think is related to arithmetic progressions in $mathbb{Z}$. After learning a nice proof of Van der Waerden’s Theorem, and sharing it with colleagues, Daniel Soukup asked a nice question about Van der Waerden’s Theorem on $omega_1$. We answered it, and the example was sufficiently nice that I would like to share it.