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STRONG COMPACTNESS, SQUARE, GCH, AND WOODIN CARDINALS
Published online by Cambridge University Press: 26 August 2022
Abstract
We show the consistency, relative to the appropriate supercompactness or strong compactness assumptions, of the existence of a non-supercompact strongly compact cardinal $\kappa _0$ (the least measurable cardinal) exhibiting properties which are impossible when $\kappa _0$ is supercompact. In particular, we construct models in which $\square _{\kappa ^+}$ holds for every inaccessible cardinal $\kappa $ except $\kappa _0$, GCH fails at every inaccessible cardinal except $\kappa _0$, and $\kappa _0$ is less than the least Woodin cardinal.
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- © The Author(s), 2022. Published by Cambridge University Press on behalf of The Association for Symbolic Logic