Bounded Martin's Maximum, Weak ErdoS cardinals, and ψ

David Asperó, Philip D. Welch

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


We prove that a form of the Erdos property (consistent with V = L[H] and strictly weaker than the Weak Chang's Conjecture at ?), together with Bounded Martin's Maximum implies that Woodin's principle ? holds, and therefore 2 = ?. We also prove that ? implies that every function f: ? ? ? is bounded by some canonical function on a club and use this to produce a model of the Bounded Semiproper Forcing Axiom in which Bounded Martin's Maximum fails.
Original languageEnglish
Pages (from-to)1141-1152
Number of pages12
JournalJournal of Symbolic Logic
Issue number3
Publication statusPublished - 1 Sep 2002


  • ψAC
  • Bounded Martin's Maximum
  • Bounding by canonical functions
  • Erdos cardinals

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