Reflecting ordinal

A cardinal \(\kappa\) is \(\Pi^n_m\)-reflecting if for every \(\Pi_m\) formula \(\phi(x)\), and \(b\in L_\alpha\), if \((L_\alpha,\in)\models\varphi(b)\) there exists a \(\beta<\alpha\) such that \(b\in L_\beta\) and \((L_\beta,\in)\models\phi(b)\). These are similar to the Indescribable cardinals.