 By Theorem 14, if \(\theta\) is a sentence, and \(s_1, s_2\), are any two variable-assignments, then \(M,s_1 \vDash \theta\) if and only if \(M,s_2 \vDash \theta\). So we can just write \(M\vDash \theta\) if \(M,s\vDash \theta\) for some, or all, variable-assignments \(s\). So we define 