special Aronszajn trees

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I have found two different definitions for Aronszajn special trees: somewhere they say they are Aronszajn trees where there exists a strictly increasing function from the tree to the rational numbers, somewhere else they say they are Aronszajn trees which are union of $\omega$ antichains.

What's the difference between the two definition? And in case they are equivalent, why are they? Because I can't figure it out.

Thank you very much for your help!