Title of article :
On guessing generalized clubs at the successors of regulars
Author/Authors :
Rinot، نويسنده , , Assaf، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2011
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.
mentary 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.
o 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.
Keywords :
Generalized clubs , Souslin tree , diamond , Non-saturation , Uniformization , Club guessing
Journal title :
Annals of Pure and Applied Logic
Journal title :
Annals of Pure and Applied Logic