Guessing clubs in the generalized club filter
Volume 195 / 2007
Fundamenta Mathematicae 195 (2007), 177-191
MSC: 03E05, 03E40.
DOI: 10.4064/fm195-2-5
Abstract
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 $[\lambda]^{\aleph_0}$.
