Fragility and indestructibility II

Spencer Unger*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 the 'superdestructibility' theorems of Hamkins and Shelah.(3)An answer to a question from our previous paper on the apparent consistency strength of the assertion "The tree property at ℵ2 is indestructible under ℵ2-directed closed forcing".(4)Two models for successive failures of weak square on long intervals of cardinals.

Original languageEnglish
Pages (from-to)1110-1122
Number of pages13
JournalAnnals of Pure and Applied Logic
Issue number11
StatePublished - 1 Nov 2015
Externally publishedYes


  • Forcing
  • Fragility
  • Indestructibility
  • Large cardinals
  • Tree property


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