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

  • David Asperó (a1) and Philip D. Welch (a2)


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.



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

  • David Asperó (a1) and Philip D. Welch (a2)


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