A universal Aronszajn line

A universal model of a certain class is a model in the class containing isomorphic copy of any other model of that class. In this talk, we concentrate in some subclasses of linear orders at w1. First, we address the question for the scattered order and get a negative answer. Going forward to a more complex class- Aronszajn lines, in his 2006 celebrated paper Justin Moore proved that under PFA there exists a two element basis of the class of Aronszajn lines. We shall review a sequel paper which utilizes this result, and shows that existence of such a basis entails a universal order for this class.