Chang's conjecture for \(\aleph_\omega\)
From huge-like large cardinal assumptions, the relative consistency of \((\aleph_{\omega_ n+1},\aleph_{\omega_ n})\twoheadrightarrow (\aleph_{k+1},\aleph_ k)\) for \(k=n<\omega\) or \(k+1<n<\omega\) is shown (with GCH). Under GCH, a simple argument shows that the case \(n<k\) is false. Open remains the case when \(k+1=n\).
scientific article; zbMATH DE number 4139730