In mathematical logic, the compactness theorem states that a (possibly infinite) set of first-order sentences has a model, iff every finite subset of it has a model. There is a generalization of compactness for languages that are of higher order than first-order ones. With respect to theories based on logics that are strictly stronger than first-order logic, compactness is seen to be too strong a property.
The compactness theorem for the propositional calculus is a result of Tychonoff's theorem (which says that the product of compact spaces is compact) applied to compact Stone spaces; hence the theorem's name.
Reference:
http://en.wikipedia.org/wiki/Compactness_theorem
