Abstract
Woodin has shown that if there is a measurable Woodin cardinal then there is, in an appropriate sense, a sharp for the Chang model. We produce, in a weaker sense, a sharp for the Chang model using only the existence of a cardinal \(\kappa \) having an extender of length \(\kappa ^{+\omega _1}\).
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This paper is dedicated to the memory of Rich Laver and Jim Baumgartner, who I treasured as friends, colleagues and exemplars since we were graduate students together.
I would like to thank the Mitlag Leffler Institute, where this work was conceived while the author was resident at the program Mathematical Logic: Set theory and model theory in 2009, and the Fields Institute, where much of the work on this paper was done while the author participated in the Thematic Program on Forcing and its Applications in Fall 2012.
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Mitchell, W.J. The sharp for the Chang model is small. Arch. Math. Logic 56, 935–982 (2017). https://doi.org/10.1007/s00153-017-0547-6
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DOI: https://doi.org/10.1007/s00153-017-0547-6