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

Published online by Cambridge University Press:  12 March 2014

David Asperó  and
Philip D. Welch
David Asperó
Affiliation:
Institut Für Formale Logik, Universität Wien, Währingerstr. 25, A-1090 Wien, Austria, E-mail: aspero@logic.univie.ac.at
Philip D. Welch
Affiliation:
Institut Für Formale Logik, Universität Wien, Währingerstr. 25, A-1090 Wien, Austria, E-mail: welch@logic.univie.ac.at
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Abstract

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.

Keywords

Bounded Martin's MaximumψACbounding by canonical functionsErdӧs cardinals
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 3 , September 2002 , pp. 1141 - 1152
Copyright
Copyright © Association for Symbolic Logic 2002

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