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Some results about (+) proved by iterated forcing

  • Tetsuya Ishiu (a1) and Paul B. Larson (a1)


We shall show the consistency of CH+⌝(+) and CH+(+)+there are no club guessing sequences on ω 1. We shall also prove that ◊+ does not imply the existence of a strong club guessing sequence on ω 1.



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[1] Ishiu, T., Club guessing sequences and filters, this Journal, vol. 70 (2005), no. 4, pp. 10371071.
[2] Larson, P., The canonical function game, Archive for Mathematical Logic, vol. 44 (2005), no. 7, pp. 817827.
[3] Moore, Justin Tatch, ω1 and −ω1 may be the only minimal uncountable linear orders, Michigan Mathematical Journal, vol. 55 (2007), no. 2, pp. 437457.
[4] Shelah, Saharon, Proper and improper forcing, second ed., Perspectives in Mathematical Logic, Springer-Verlag, Berlin, 1998.
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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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