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The study of canonical inner models for large cardinal hypotheses, with particular attention to their fine structure theory, and iterability issues.

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A Weak form of Extendibility and Inner Model Theory

Let a cardinal $\kappa$ be $n$-shadow iff $\kappa$ does not have cofinality $\omega$ and for any $n$-th order sentence $\varphi$ in the language $\mathcal{L}_\in$, $\varphi\Leftrightarrow V_\kappa\mod …
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