Full Idea
Classical logical consequence is compact, which means that any consequence of an infinite set of propositions (such as a theory) is a consequence of some finite subset of them.
Gist of Idea
Compactness is when any consequence of infinite propositions is the consequence of a finite subset
Source
Stephen Read (Thinking About Logic [1995], Ch.2)
Book Reference
Read,Stephen: 'Thinking About Logic' [OUP 1995], p.43