In this paper we continue work from a previous paper on the fragility and indestructibility of the tree property. We present the following: (1) A preservation lemma implicit in Mitchell’s PhD thesis, which generalizes all previous versions of Hamkins’ Key lemma. (2) A new proof of theorems the ‘superdestructibility’ theorems of Hamkins and Shelah. (3) An answer to a question from our previous p...
