On guessing generalized clubs at the successors of regulars
Abstract: Konig, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of an higher Souslin tree from the strong guessing principle.
Complementary to the author’s work on the validity of diamond and non-saturation at the successor of singulars, we deal here with successor of regulars. It is established that even the non-strong guessing principle entails non-saturation, and that, assuming the necessary cardinal arithmetic configuration, entails a diamond-type principle which suffices for the construction of an higher Souslin tree.
We also establish the consistency of GCH with the failure of the weakest form of generalized club guessing. This, in particular, settles a question from the original paper.
A. Rinot, On guessing generalized clubs at the successors of regulars, Ann. Pure Appl. Logic, 162(7): 566-577, 2011.
This entry was posted in Publications, Souslin Hypothesis, Squares and Diamonds
and tagged 03E05
, Club Guessing
, Generalized Clubs
, Kurepa Hypothesis
, Souslin Tree
, Successor of Regular Cardinal
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