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Unfoldable cardinals and the GCH

  • Joel David Hamkins (a1) (a2)

Unfoldable cardinals are preserved by fast function forcing and the Laver-like preparations that fast functions support. These iterations show, by set-forcing over any model of ZFC, that any given unfoldable cardinal κ can be made indestructible by the forcing to add any number of Cohen subsets to κ.

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[Ham98]Hamkins Joel David, Gap forcing, submitted.
[Ham]Hamkins Joel David, The lottery preparation, Annals of Pure and Applied Logic, to appear.
[Ham97]Hamkins Joel David, Canonical seeds and Prikry trees, this Journal, vol. 62 (1997), no. 2, pp. 373396.
[Ham99]Hamkins Joel David, Gap forcing: generalizing the Levy-Solovay theorem, The Bulletin of Symbolic Logic, vol. 5 (1999), no. 2, pp. 264272.
[Vil98]Villaveces Andres, Chains of end elementary extensions of models of set theory, this Journal, vol. 63 (1998), no. 3, pp. 11161136.
[VL99]Villaveces Andres and Leshem Amir, The failure of the GCH at unfoldable cardinals, preprint.
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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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