Definition:Consistent (Logic)/Set of Formulas

Definition
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 $\mathscr P$ :


 * 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 $\FF$.

Also see

 * Definition:Satisfiable Set of Formulas