Answer by Yair Hayut for Is every transitive ZF-model of inaccessible height...
Theorem: Let $\kappa$ be strongly inaccessible in $V$, such that $V \models ZFC$. If $M\models ZF$, then $L(M) \cap V_\kappa = M$.Proof: Let us prove by induction on $\alpha < \kappa$ that $L(M)...
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Let $\kappa$ be an inaccessible cardinal and let $M \subseteq V_{\kappa}$ be an inner model of $V_{\kappa}$, i.e., a transitive model of $\mathsf{ZF}$ containing all the ordinals up to $\kappa$. My...
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