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Core models in the presence of Woodin cardinals. (English) Zbl 1109.03064
Summary: Let $$0<n<\omega$$. If there are $$n$$ Woodin cardinals and a measurable cardinal above, but $$M^\#_{n+1}$$ does not 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 $$K$$.

##### MSC:
 3e+45 Inner models, including constructibility, ordinal definability, and core models 3e+55 Large cardinals
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##### References:
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