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Controlling the number of normal measures at successor cardinals
Mathematical Logic Quarterly 68 (3):304-309 (2022)
Abstract
We examine the number of normal measures a successor cardinal can carry, in universes in which the Axiom of Choice is false. When considering successors of singular cardinals, we establish relative consistency results assuming instances of supercompactness, together with the Ultrapower Axiom (introduced by Goldberg in [12]). When considering successors of regular cardinals, we establish relative consistency results only assuming the existence of one measurable cardinal. This allows for equiconsistencies.Other Versions
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References found in this work
Sets constructible from sequences of ultrafilters.William J. Mitchell - 1974 - Journal of Symbolic Logic 39 (1):57-66.
$K$ without the measurable.Ronald Jensen & John Steel - 2013 - Journal of Symbolic Logic 78 (3):708-734.
The number of normal measures.Sy-David Friedman & Menachem Magidor - 2009 - Journal of Symbolic Logic 74 (3):1069-1080.
The linearity of the Mitchell order.Gabriel Goldberg - 2018 - Journal of Mathematical Logic 18 (1):1850005.
Inverse limit reflection and the structure of L.Scott S. Cramer - 2015 - Journal of Mathematical Logic 15 (1):1550001.
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