Erdős Problem 70: Let $\mathfrak{c}$ be the cardinality of the continuum, let $\beta$ be a countable ordinal, and let $2 \le n < \omega$. Is it true that $\mathfrak{c} \to (\beta, n)^3_2$?

**The relation at $\omega_1$**: $\mathfrak{c} \to (\omega_1, n)^3_2$ for finite $n \ge 2$, where $\omega_1 = \aleph_1$ is the first uncountable ordinal.

Note that $\omega_1$ is *not* a countable ordinal, so this is not directly an instance of the main Erdős problem (which asks for *countable* $\beta$). Under CH, $\omega_1 = \mathfrak{c}.\mathrm{ord}$, making this a self-referential question about $\mathfrak{c}.\mathrm{ord} \to (\mathfrak{c}.\mathrm{ord}, n)^3_2$.