We revisit the classic theorem of J. T. Moore that PFA implies Shelah's conjecture. Using new preservation results related to proper forcing, forcing iterations, and trees, we settle some long-standing open questions in the literature concerning this theorem, including: (1) BPFA implies the existence of a five element basis for the uncountable linear orders, and (2) an inaccessible cardinal is equiconsistent with the conjunction of the existence of a five element basis for the uncountable linear orders and Aronszajn tree saturation. The talk is intended to complement lectures given by Moore at the Cornell logic seminar on the same topic in Fall 2025. This work is joint with Moore.