Characterization of trees admitting narrow subsystems

Characterize which trees admit narrow subsystems.

Background

The paper proves that a tree with a narrow subsystem must contain a well-pruned subtree, but this is only a necessary condition and does not characterize the trees that admit narrow subsystems.

A characterization could simplify the construction of narrow systems used in results on the tree property and strong tree property, especially at successors of singular cardinals, where locating a narrow subsystem is a major source of difficulty.

References

We are also interested in a much more general version of this question: Which trees admit narrow subsystems?

— A Note on Narrow Systems  (2610.00934 - Adkisson, 1 Oct 2026) in Section 1, Introduction

On the other hand, it is unknown to the author whether it is consistent for either of these trees to admit a narrow system.

— A Note on Narrow Systems  (2610.00934 - Adkisson, 1 Oct 2026) in Section 4, “Some Well-Pruned Wide Aronszajn Trees,” final paragraph