Trees generated by narrow concrete systems

Characterize, up to isomorphism, the trees that can be generated by narrow concrete systems.

Background

For a concrete one-cardinal system, the generated tree is obtained canonically by adding all initial segments of system elements. The generated tree can be substantially wider than the original system, even when the system has finite width.

The paper therefore asks for a structural characterization of the trees obtainable in this way, a problem distinct from determining whether such generated trees possess cofinal branches.

References

Which trees (up to isomorphism) can be generated by narrow concrete $$-systems?

— A Note on Narrow Systems  (2610.00934 - Adkisson, 1 Oct 2026) in Section 2, subsection “One-cardinal objects,” immediately after the definition of the tree generated from a concrete system

Do all $(,)$-trees generated from narrow systems contain a thin subtree?

— A Note on Narrow Systems  (2610.00934 - Adkisson, 1 Oct 2026) in Section 2, subsection “Two-cardinal objects,” immediately after the question about Theorem \ref{thm:LH}