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I am asking for a reference request/proof sketch for the result of Steel that characterizes $L[T_{2n+1}]$ as a direct limit of mice.

Given that both $L[T_{2n+1}]$ and $M_{2n}$ have a $\Sigma_{2n+2}$ well-ordering of the reals, I think the result should be that $L[T_{2n+1}]$ is the direct limit of iterable mice with $2n$ Woodin cardinals, but I am not sure.

I'm starting to think that this result is not written up, in which case a proof sketch would be appreciated.

Thank you for your help!

Cody

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  • $\begingroup$ This result is mentioned in Steel's paper "$HOD^{L(R)}$ is a core model below $\Theta$". It is not proved explicitly there but the same method applies. $\endgroup$ Oct 15, 2015 at 15:52

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