Core Models in the Presence of Woodin Cardinals

Journal of Symbolic Logic 71 (4):1145 - 1154 (2006)
Abstract
Let 0 < n < ω. If there are n Woodin cardinals and a measurable cardinal above, but $M_{n+1}^{\#}$ doesn't exist, then the core model K exists in a sense made precise. An Iterability Inheritance Hypothesis is isolated which is shown to imply an optimal correctness result for K
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