Strong tree property and failure of SCH

Determine whether it is consistent for the Singular Cardinal Hypothesis to fail above a cardinal carrying the strong tree property.

Background

The paper discusses the close relationship between the strong tree property and strong compactness, together with results showing that stronger principles such as ISP imply SCH above the relevant cardinal. Lambie-Hanson’s narrow system results also imply SCH under a narrow system property that holds in all currently known models of the strong tree property.

The unresolved issue is whether the strong tree property alone can coexist with failure of SCH above the cardinal. A positive implication from the strong tree property to the relevant narrow system property would settle this question negatively.