Abstract
König, Larson and Yoshinobu initiated the study of principles for guessing generalized clubs, and introduced a construction of a 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 a 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 a 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.
Original language | American English |
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Pages (from-to) | 566-577 |
Number of pages | 12 |
Journal | Annals of Pure and Applied Logic |
Volume | 162 |
Issue number | 7 |
DOIs | |
State | Published - 1 Jun 2011 |
Externally published | Yes |
Keywords
- Club guessing
- Diamond
- Generalized clubs
- Non-saturation
- Souslin tree
- Uniformization
All Science Journal Classification (ASJC) codes
- Logic