 Theorem 17. Let \(\Gamma\) be a set of sentences. The following are equivalent: (a) \(\Gamma\) is satisfiable; (b) there is no sentence \(\theta\) such that both \(\Gamma \vDash \theta\) and \(\Gamma \vDash \neg \theta\); (c) there is some sentence \(\psi\) such that it is not the case that \(\Gamma \vDash \psi\).