>[!info] Definition >A cardinal $\kappa$ is *second order describable with respect to measurables* if there is a second order formula $\Phi(X)$ and $A \subseteq V_{\kappa}$ such that >- $(V_{\kappa},\in) \vDash \Phi(A)$ >- For every measurable $\lambda<\kappa$, $(V_{\lambda},\in) \vDash \neg \Phi(A\cap V_{\lambda})$ >[!note] Remark >If $\kappa$ has [[Mitchell rank and Mitchell order|Mitchell rank]] gt;1$ then it is second order *indescribable* wrt measurables. >[!info] Definition >A mouse is *narrow* if it does not contain measurable-indescribable cardinals.