A universal Aronszajn line

The purpose of this note is to define an Aronszajn line $\eta_C$ and prove that under the assumption of $\PFA$ it is universal for the class of Aronszajn lines. Moreover $\eta_C$ can be easily described in terms of a fixed Countryman type $C$: it is the direct limit of the finite lexicographic products of the form $C \times (-C) \times \ldots \times (\pm C)$.

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Published 1 January 2009