I was reading Chapter 3 - Coherent Sequences - in Handbook of Set Theory and it says that every subtree of $\sigma \Bbb{Q}$ which is finitely branching at limit nodes is easily seen to be a special tree (bottom, page 220). Why is that so obvious?
Here $\Bbb Q$ is $\omega^{<\omega}$ ordered by the right lexicographical ordering $<_r$: $s<_rt$ if $s$ is an end-extension of $t$, or if $s(i)<t(i)$ for $i=\min\{j:s(j)\ne t(j)\}$. $\sigma\Bbb Q$ is the tree of all well-ordered subsets of $\Bbb Q$, ordered by end-extension. A PDF of this chapter of the Handbook is available here in case the Google Books link doesn’t work for you.