The proper forcing axiom is shown to imply that a compact scattered sequential space with scattering height at most $\omega_1$ must have sequential order at most $\omega$.
Sequential order, scattered spaces, PFA
DOW, ALAN and TOKGÖZ, SEÇİL
"More on sequential order of compact scattered spaces,"
Turkish Journal of Mathematics: Vol. 42:
3, Article 38.
Available at: https://journals.tubitak.gov.tr/math/vol42/iss3/38