Category:Consistency of Logical Formulas has Finite Character

This category contains pages concerning Consistency of Logical Formulas has Finite Character:

Let $P$ be the property of collections of logical formulas defined as:

$\forall \FF: \map P \FF$ denotes that $\FF$ is consistent.

Then $P$ is of finite character.

That is:

$\FF$ is a consistent set of formulas if and only if every finite subset of $\FF$ is also a consistent set of formulas.