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2 results

  • Bounded Martin's Maximum, weak Erdӧs cardinals, and ψAc

  • David Asperó, Philip D. Welch
  • Journal:
    The Journal of Symbolic Logic / Volume 67 / Issue 3 / September 2002
    Published online by Cambridge University Press:
    12 March 2014, pp. 1141-1152
    Print publication:
    September 2002

  • We prove that a form of the Erdӧs property (consistent with V = L[Hω2] and strictly weaker than the Weak Chang's Conjecture at ω1), together with Bounded Martin's Maximum implies that Woodin's principle ψAC holds, and therefore . We also prove that ψAC implies that every function f: ω1 → ω1 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.