Bounded Martin's Maximum, weak Erdõs cardinals, and ψAC

D Asperó, PD Welch

Research output: Contribution to journalArticle (Academic Journal)peer-review

6 Citations (Scopus)

Abstract

We prove that a form of the Erdos property (consistent with V = L[H-omega2] and strictly weaker than the weak Chang's Conjecture at omega(1)), together with Bounded Martin's Maximum implies that Woodin's principle psi(AC) holds, and therefore 2(N0) = N-2. We also prove that psi(AC) implies that every function f : omega(1) --> omega(1) 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.
Translated title of the contributionBounded Martin's Maximum, weak Erdõs cardinals, and ψAC
Original languageEnglish
Pages (from-to)1141 - 1152
Number of pages12
JournalJournal of Symbolic Logic
Volume67 (3)
Publication statusPublished - Sep 2002

Bibliographical note

Publisher: Assn Symbolic Logic Inc

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