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A note on tall cardinals and level by level equivalence
Mathematical Logic Quarterly 62 (1-2):128-132 (2016)
Abstract
Starting from a model “κ is supercompact” + “No cardinal is supercompact up to a measurable cardinal”, we force and construct a model such that “κ is supercompact” + “No cardinal is supercompact up to a measurable cardinal” + “δ is measurable iff δ is tall” in which level by level equivalence between strong compactness and supercompactness holds. This extends and generalizes both [, Theorem 1] and the results of.Other Versions
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References found in this work
How large is the first strongly compact cardinal? or a study on identity crises.Menachem Magidor - 1976 - Annals of Mathematical Logic 10 (1):33-57.
On certain indestructibility of strong cardinals and a question of Hajnal.Moti Gitik & Saharon Shelah - 1989 - Archive for Mathematical Logic 28 (1):35-42.
Identity crises and strong compactness : II. Strong cardinals.Arthur W. Apter & James Cummings - 2001 - Archive for Mathematical Logic 40 (1):25-38.
Identity crises and strong compactness.Arthur Apter & James Cummings - 2000 - Journal of Symbolic Logic 65 (4):1895-1910.
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