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Superdestructibility: A dual to Laver's indestructibility

  • Joel David Hamkins (a1) (a2) and Saharon Shelah (a3)

After small forcing, any <κ-closed forcing will destroy the supercompactness and even the strong compactness of κ.

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[1]Hamkins, Joel David, Small forcing makes any cardinal superdestructible, to appear in this Journal.
[2]Ketonen, Jussi, Strong compactness and other cardinal sins, Annals of Mathematical Logic, vol. 5 (1972), pp. 4776.
[3]Laver, Richard, Making the supercompactness of κ indestructible under κ-directed closed forcing, Israel Journal of Mathematics, vol, 29 (1978), pp. 385388.
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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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