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On guessing generalized clubs at the successors of regulars
Authors:Assaf Rinot
Institution:
  • School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
  • 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.
    Keywords:primary  03E35  secondary  03E05  03E65
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