It is well-known that the following reflection principle is consistent relative to a supercompact:
For all $\kappa \geq \omega_2$ and all stationary $S \subseteq [\kappa]^\omega$, there is $X \subseteq \kappa$ such that $\omega_1 \subseteq X$, $|X| = \omega_1$, and $S \cap [X]^\omega$ is stationary.
Let us say $Refl(\kappa,\mu)$ holds when:
For all stationary $S \subseteq [\kappa]^\omega$, there is $X \subseteq \kappa$ such that $\mu \subseteq X$, $|X| = \mu$, and $S \cap [X]^\omega$ is stationary.
If $\mu$ is regular and there is a supercompact above $\mu$, then by Levy-collapsing that supercompact to be $\mu^+$, we get a model of $(\forall \kappa \geq \mu^+)Refl(\kappa,\mu)$.
Question: Is $Refl(\aleph_{\omega+1},\aleph_\omega)$ consistent?
