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#### An accessibility theorem for infinite graph minors

We prove the following recent conjecture of Halin. Let $\Gamma_0$
be the class of all graphs, and for every ordinal $\mu>0$ let
$\Gamma_\mu$ be the class of all graphs containing infinitely
many disjoint connected graphs from~$\Gamma_\lambda$, for every
$\lambda < \mu$. Then a graph lies in all these classes $\Gamma_\mu$
if and only if it contains a subdivision of the infinite binary
tree.

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