Modal equivalence of infinite Humberstone frames and Kripke frames

Determine whether every infinite Humberstone frame is modally equivalent to some Kripke frame, i.e., whether each infinite Humberstone frame validates exactly the same modal formulas as a suitably constructed Kripke frame.

Background

The paper contrasts the expressive power of various frame classes (Kripke, Humberstone, and full possibility frames). For finite cases, atom structures can often bridge these classes, but for the infinite case it is unclear whether Humberstone frames collapse to Kripke frames under modal equivalence. Clarifying modal equivalence would settle how far Humberstone’s strengthening of the refinement–accessibility interplay extends beyond Kripke semantics.