These notes are based on results presented by Itay Neeman at the Appalachian Set Theory workshop on February 28, 2009. Spencer Unger was the official note-taker and based these notes closely on Neeman’s lectures. The purpose of the workshop was to present a recent theorem due to Neeman [16]. Theorem 1. From large cardinals, it is consistent that there is a singular strong limit cardinal κ of cofinality ω such that the Singular Cardinal Hypothesis fails at κ and the tree property holds at κ. The purpose of these notes is to give the reader the flavor of the argument without going into the complexities of the final proof in [16]. Having read these notes, the motivated reader should be prepared to understand the full argument. We begin with a discussion of trees, which are natural objects in infinite combinatorics. One topic of interest is whether a tree has a cofinal branch. For completeness we recall some definitions. Definition 2. Let λ be a regular cardinal and κ be a cardinal. 1. A λ-tree is a tree of height λ with levels of size less than λ.