  We show that under the proper forcing axiom the class of all Aronszajn lines
behave like $\sigma$-scattered orders under the embeddability relation. In
particular, we are able to show that the class of better quasi order labeled
fragmented Aronszajn lines is itself a better quasi order. Moreover, we show
that every better quasi order labeled Aronszajn line can be expressed as a
finite sum of labeled types which are algebraically indecomposable. By encoding
lines with finite labeled trees, we are also able to deduce a decomposition
result, that for every Aronszajn line $L$ there is integer n such that for any
finite colouring of $L$ there is subset $L^\prime$ of $L$ isomorphic to $L$
which uses no more than n colours.
