On guessing generalized clubs at the successors of regulars

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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 languageAmerican English
Pages (from-to)566-577
Number of pages12
JournalAnnals of Pure and Applied Logic
Volume162
Issue number7
DOIs
StatePublished - 1 Jun 2011
Externally publishedYes

Keywords

  • Club guessing
  • Diamond
  • Generalized clubs
  • Non-saturation
  • Souslin tree
  • Uniformization

All Science Journal Classification (ASJC) codes

  • Logic

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