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

David Asperó; Philip D. Welch

doi:10.2178/jsl/1190150154

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

David Asperó, Philip D. Welch

Algebra, Number Theory, Logic, and Representations (ANTLR)

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

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 language	English
Pages (from-to)	1141-1152
Number of pages	12
Journal	Journal of Symbolic Logic
Volume	67
Issue number	3
DOIs	https://doi.org/10.2178/jsl/1190150154
Publication status	Published - 1 Sept 2002

Keywords

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

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10.2178/jsl/1190150154

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

Abstract

Keywords

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