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 an integer n such that for any finite coloring of L there is subset L' of L isomorphic to L which uses no more than n colors.
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