Describes a system of logic in a language $ℒ$ if it satisfies the following condition, where $\Gamma$ is any set of sentences in $ℒ$:

• • if every finite subset of $\Gamma$ has a model, so does $\Gamma$

where a model for a set of sentences is an interpretation for the logic which makes all the sentences in the set true. Classical first-order logic is compact. (This is usually called the Compactness Theorem.) Classical second-order logic is not.