With respect to a deductive system $\text{L}$ and a set of sentences $\Gamma$, the smallest set ${\Gamma }^{{⊢}_{\text{L}}}\supseteq \Gamma$ closed under $\text{L}$-consequence. Formally, this is a set ${\Gamma }^{{⊢}_{\text{L}}}$ such that $\phi \in {\Gamma }^{{⊢}_{\text{L}}}$ if and only if ${\Gamma }^{{⊢}_{\text{L}}}{⊢}_{\text{L}}\phi$. If a set $\Gamma$ is equal to its deductive closure, it is said that $\Gamma$ is deductively closed.