The purpose of this note is to demonstrate that a weak form of club guessing on ω1 implies the existence of an Aronszajn line with no Countryman suborders. An immediate consequence is that the existence of a five element basis for the uncountable linear orders does not follow from the forcing axiom for ω-proper forcings.
"Aronszajn lines and the club filter." J. Symbolic Logic 73 (3) 1029 - 1035, September 2008. https://doi.org/10.2178/jsl/1230396763