This will be the second talk in a series about recent work on the tree property. Continuing work from last week, I will begin by sketching the end of Mitchell's argument. I will give particular attention to the branch lemmas used, where a branch lemma is a statement of the form `Forcing with property X cannot add a branch through a tree of type Y.' I will then present a new theorem that the tree property in Mitchell's model is indestructible under certain kinds of forcing. To do this I will need a new branch lemma that is essentially a generalization of a lemma we used in Mitchell's argument. If time permits I will sketch the proof of this new lemma.