Unbalanced polarized relations

We prove the consistency of relation ( μ + class="MJX-TeXAtom-CLOSE"> minsize="1.2em">) ↛ ω<!-- ω <mml:mn>1 \binom {\mu ^+}{\mu }\nrightarrow \binom ^+\ \omega _1}{\mu \quad \mu } where alttext="mu"> encoding="application/x-tex">\mu is a strong limit singular cardinal countable cofinality. This result can be forced at alttext="mu equals normal alef Subscript omega"> = ℵ<!-- ℵ encoding="application/x-tex">\mu =\aleph _\omega .