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Core Models in the Presence of Woodin Cardinals

Ralf Schindler
The Journal of Symbolic Logic
Vol. 71, No. 4 (Dec., 2006), pp. 1145-1154
Stable URL: http://www.jstor.org/stable/27588507
Page Count: 10
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Core Models in the Presence of Woodin Cardinals
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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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