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September 2009 The number of normal measures
Sy-David Friedman, Menachem Magidor
J. Symbolic Logic 74(3): 1069-1080 (September 2009). DOI: 10.2178/jsl/1245158100


There have been numerous results showing that a measurable cardinal κ can carry exactly α normal measures in a model of GCH, where α is a cardinal at most κ++. Starting with just one measurable cardinal, we have [9] (for α=1), [10] (for α= κ++, the maximum possible) and [1] (for α=κ⁺, after collapsing κ++). In addition, under stronger large cardinal hypotheses, one can handle the remaining cases: [12] (starting with a measurable cardinal of Mitchell order α), [2] (as in [12], but where κ is the least measurable cardinal and α is less than κ, starting with a measurable of high Mitchell order) and [11] (as in [12], but where κ is the least measurable cardinal, starting with an assumption weaker than a measurable cardinal of Mitchell order 2). In this article we treat all cases by a uniform argument, starting with only one measurable cardinal and applying a cofinality-preserving forcing. The proof uses κ-Sacks forcing and the “tuning fork” technique of [8]. In addition, we explore the possibilities for the number of normal measures on a cardinal at which the GCH fails.


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Sy-David Friedman. Menachem Magidor. "The number of normal measures." J. Symbolic Logic 74 (3) 1069 - 1080, September 2009.


Published: September 2009
First available in Project Euclid: 16 June 2009

zbMATH: 1183.03042
MathSciNet: MR2548481
Digital Object Identifier: 10.2178/jsl/1245158100

Rights: Copyright © 2009 Association for Symbolic Logic


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Vol.74 • No. 3 • September 2009
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