compactness

A logic is said to be $(\kappa ,\lambda )$-compact, if the following holds

If $\mathrm{\Phi }$ is a set of sentences of cardinality less than or equal to $\kappa$ and all subsets of $\mathrm{\Phi }$ of cardinality less than $\lambda$ are consistent, then $\mathrm{\Phi }$ is consistent.

For example, first order logic is $(\omega ,\omega )$-compact, for if all finite subsets of some class of sentences are consistent, so is the class itself.