Full Idea
Compactness does not deny that an inference can have infinitely many premisses. It can; but classically, it is valid if and only if the conclusion follows from a finite subset of them.
Gist of Idea
Compactness does not deny that an inference can have infinitely many premisses
Source
Stephen Read (Thinking About Logic [1995], Ch.2)
Book Reference
Read,Stephen: 'Thinking About Logic' [OUP 1995], p.43