Compactness Theorem for Boolean Interpretations

Theorem
Let $\mathbf H$ be a countable set of WFFs of propositional logic.

Suppose $\mathbf H$ is finitely satisfiable for boolean interpretations.

That is, suppose that every finite subset $\mathbf H' \subseteq \mathbf H$ is satisfiable for boolean interpretations.

Then $\mathbf H$ has a model.

Also known as
This result is also known as the Compactness Theorem of Propositional Logic, but as there are multiple semantics for propositional logic, this name is too general to be used on.