A definable failure of the singular cardinal hypothesis (Q1936814)

The authors make good on what the title of the paper promises: a model in which \(\aleph_\omega\) is a strong limit, \(2^{\aleph_\omega}>\aleph_{\omega+1}\), and \(H(\aleph_{\omega+1})\) has a (lightface) definable wellorder. The method used is to create a similar situation at a measurable cardinal and then collapse this measurable to~\(\aleph_\omega\), while preserving the statements above.