On a convenient property about [γ]

Research output: Contribution to journalArticlepeer-review


Several situations are presented in which there is an ordinal ? such that is a stationary subset of for all stationary subset of [?] for all stationary S,T ??. A natural strengthening of the existence of an ordinal ? for which the above conclusion holds lies, in terms of consistency strength, between the existence of the sharp of and the existence of sharps for all reals. Also, an optimal model separating Bounded Semiproper Forcing Axiom (BSPFA) and Bounded Martin's Maximum (BMM) is produced and it is shown that a strong form of BMM involving only parameters from Himplies that every function from ? into ? is bounded on a club by a canonical function.
Original languageEnglish
Pages (from-to)653-677
Number of pages25
JournalArchive for Mathematical Logic
Issue number7
Publication statusPublished - 1 Sep 2009


  • 03E05
  • 03E57
  • 03E55
  • 03E35

Cite this