I am doing some exercises from Kunen's book "Set Theory", I'm having problems with exercise 39 from page 90, the exercise goes like this: Show that any Aronszajn tree which is a subtree of \{ s \in \omega^{< \omega_1}: s is $1-1\}$ cannot be Suslin tree. Hint: For each $n \in \omega$, $\{s \in T: \exists \alpha (dom(s)= \alpha + 1 \wedge s(\alpha)=n)\}$ is an antichain.
Can anyone help me with this exercise? PLEASE!