TITLE: Reference for Chang's Conjecture at $\aleph_{\omega}$
QUESTION [6 upvotes]: The following theorem is well known:
Theorem: $(\aleph_{\omega + 1}, \aleph_{\omega}) \not\twoheadrightarrow  (\aleph_{n + 1}, \aleph_n)$ for every $n \geq 3$. Under CH, $(\aleph_{\omega + 1}, \aleph_{\omega}) \not\twoheadrightarrow (\aleph_{n + 1}, \aleph_n)$ for every $n > 0$.
where $(\kappa, \lambda)\twoheadrightarrow (\mu, \nu)$ stands for Chang's Conjecture between the pair of cardinals $(\kappa, \lambda)$ and the pair $(\mu, \nu)$.
Who was the first to prove this statement? 
Was it published somewhere?

REPLY [4 votes]: Levinski+Magidor+Shelah, Chang's conjecture for $\aleph_ \omega$ -- Israel J Math 69 (1990) 161-172.
See also "Some consequences of reflection on the approachability ideal" by Matteo Vilale, Assaf Sharon, Transactions of the American Mathematical Society 362, 4201-4212, 2009. In particular fact 4.2 and remarks after it.