Im working on a FOL exercise but i'm a little stuck here. Let $S$ be a symbol set and $\mathcal{J} = (\mathcal{U}, \beta)$ an $S$-interpretation. Further let $\Phi:=\{\varphi\in L^{S}|\mathcal{J}\models\varphi$}
Show that $\Phi$ is negation complete.
So i have to show that $\Phi\vdash \varphi$ or $\Phi\vdash\neg\varphi$ But i don't know where to start. Please help.