Denote by $o(\alpha)$ the [[Mitchell rank and Mitchell order|Mitchell rank]] of $\alpha$. **Theorem (Mitchell).** There exists an inner model $L[\mathcal{U}]$ such that (i) for every $\alpha, o^{L[\mathcal{U}]}(\alpha)=o^{\mathcal{U}}(\alpha)=\min \left\{o(\alpha),\left(\alpha^{++}\right)^{L[\mathcal{U}]}\right\}$; (ii) $\mathcal{U}=\left\langle U_{\alpha, \beta}: \beta<o^{\mathcal{U}}(\alpha)\right\rangle$; (iii) each $U_{\alpha, \beta}$ is in $L[\mathcal{U}]$ a normal measure of order $\beta$; (iv) every normal measure in $L[\mathcal{U}]$ is $U_{\alpha, \beta}$ for some $\alpha$ and $\beta$; (v) $L[\mathcal{U}] \vDash \mathrm{GCH}$. Let $\lambda = \sup o[\mathrm{Ord}]$. Then $L[\mathcal{U}]$ is the *canonical model for measure sequences of rank $\lambda$*. ## References [[Mitchell - Sets constructible from sequences of ultrafilters]] [[Mitchell - The core model for sequences of measures. I]] [[Jech - Set theory]] chapter 19