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Line 29: If V has Woodin cardinals but not cardinals strong past a Woodin one, then under appropriate circumstances (a candidate for) K can be constructed by constructing K below each Woodin cardinal (and below the class of all ordinals) κ but above that K as constructed below the supremum of Woodin cardinals below κ. The candidate core model is not fully iterable (iterability fails at Woodin cardinals) or generically absolute, but otherwise behaves like K. ==References== * W.H. Woodon (2001). [http://www.aimath.org/WWN/coremodel/coremodel.pdf The Continuum Hypothesis, Part I]. Notices of the AMS. [[Category:Inner model theory]]

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