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Core models in the presence of Woodin cardinals

Ralf Schindler
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Abstract

It is shown that if there is a measurable cardinal above n Woodin cardinals and M_{n+1}^# doesn't exist then K exists. K is not fully iterable, though, but only iterable with respect to stacks of certain trees living between the Woodin cardinals. However, it is still true that if M is an omega-closed iterate of V then K^M is an iterate of K.

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Ralf Schindler. 2003-03-07. Core models in the presence of Woodin cardinals. https://arxiv.org/abs/math/0303089

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