\begin{definition}[Definition:Consistent (Logic)/Set of Formulas]
Let $\LL$ be a logical language.
Let $\mathscr P$ be a proof system for $\LL$.
Let $\FF$ be a collection of logical formulas.
Then $\FF$ is '''consistent for $\mathscr P$''' {{iff}}:
:There exists a logical formula $\phi$ such that $\FF \nvdash_{\mathscr P} \phi$.
That is, some logical formula $\phi$ is '''not''' a provable consequence of $\FF$.
\end{definition}