Guessing clubs in the generalized club filter

Volume 195 / 2007

Bernhard König, Paul Larson, Yasuo Yoshinobu Fundamenta Mathematicae 195 (2007), 177-191 MSC: 03E05, 03E40. DOI: 10.4064/fm195-2-5


We present principles for guessing clubs in the generalized club filter on ${\cal P}_\kappa\lambda$. These principles are shown to be weaker than classical diamond principles but often serve as sufficient substitutes. One application is a new construction of a $\lambda^+$-Suslin-tree using assumptions different from previous constructions. The other application partly solves open problems regarding the cofinality of reflection points for stationary subsets of $[\lambda]^{\aleph_0}$.


  • Bernhard KönigDepartment of Mathematics
    University of Toronto
    Toronto, Ontario, Canada M5S 2E4
  • Paul LarsonDepartment of Mathematics and Statistics
    Miami University
    Oxford, OH 45056, U.S.A.
  • Yasuo YoshinobuGraduate School of Information Science
    Nagoya University
    Furocho, Chikusa-ku
    Nagoya 464-8601, Japan

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